| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 7.1-a1 |
7.1-a |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{5} \) |
$136.33849$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.015403341$ |
$30570.15506$ |
2.72219 |
\( \frac{20910}{49} a^{5} + \frac{324350}{49} a^{4} - \frac{61827}{7} a^{3} - \frac{1575082}{49} a^{2} + \frac{890287}{49} a + \frac{274095}{7} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 7 a + 5\) , \( a\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 2\) , \( -a^{5} - 5 a^{4} + 18 a^{3} + 19 a^{2} - 35 a - 17\) , \( 10 a^{5} - 48 a^{4} + 20 a^{3} + 147 a^{2} - 100 a - 83\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+7a+5\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-2\right){y}={x}^{3}+a{x}^{2}+\left(-a^{5}-5a^{4}+18a^{3}+19a^{2}-35a-17\right){x}+10a^{5}-48a^{4}+20a^{3}+147a^{2}-100a-83$ |
| 7.1-a2 |
7.1-a |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{10} \) |
$136.33849$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.030806683$ |
$7642.538767$ |
2.72219 |
\( \frac{207225358689}{2401} a^{5} + \frac{260903631341}{2401} a^{4} - \frac{1440312844568}{2401} a^{3} - \frac{1737027620152}{2401} a^{2} + \frac{313731722981}{343} a + \frac{369533528708}{343} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 6 a + 4\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 7 a - 2\) , \( a^{5} - a^{4} - 5 a^{3} + a^{2} + 6 a + 4\) , \( -2 a^{5} - 8 a^{4} + 22 a^{3} + 46 a^{2} - 46 a - 71\) , \( -55 a^{5} + 72 a^{4} + 256 a^{3} - 199 a^{2} - 320 a + 45\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+a^{2}+6a+4\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+a^{2}+6a+4\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+7a-2\right){x}^{2}+\left(-2a^{5}-8a^{4}+22a^{3}+46a^{2}-46a-71\right){x}-55a^{5}+72a^{4}+256a^{3}-199a^{2}-320a+45$ |
| 7.2-a1 |
7.2-a |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{5} \) |
$136.33849$ |
$(-a^5+3a^4+2a^3-9a^2+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 5 \) |
$0.015403341$ |
$30570.15506$ |
2.72219 |
\( -\frac{20910}{49} a^{5} + \frac{428900}{49} a^{4} - \frac{1073711}{49} a^{3} - \frac{102607}{7} a^{2} + 44006 a + \frac{163763}{7} \) |
\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 3\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} + 3\) , \( a^{5} - a^{4} - 6 a^{3} + 2 a^{2} + 10 a + 3\) , \( -5 a^{5} + 16 a^{4} + 15 a^{3} - 62 a^{2} - 10 a + 56\) , \( 8 a^{5} - 28 a^{4} - 16 a^{3} + 115 a^{2} - 7 a - 119\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-3a^{2}+5a+3\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+2a^{2}+10a+3\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-8a^{2}+3\right){x}^{2}+\left(-5a^{5}+16a^{4}+15a^{3}-62a^{2}-10a+56\right){x}+8a^{5}-28a^{4}-16a^{3}+115a^{2}-7a-119$ |
| 7.2-a2 |
7.2-a |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{10} \) |
$136.33849$ |
$(-a^5+3a^4+2a^3-9a^2+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.030806683$ |
$7642.538767$ |
2.72219 |
\( -\frac{207225358689}{2401} a^{5} + \frac{1297030424786}{2401} a^{4} - \frac{1675555267686}{2401} a^{3} - \frac{345755825560}{343} a^{2} + \frac{502732913476}{343} a + \frac{296235041019}{343} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 5 a\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 3 a^{2} - 2 a - 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( 16 a^{5} - 79 a^{4} + 55 a^{3} + 179 a^{2} - 142 a - 103\) , \( 59 a^{5} - 278 a^{4} + 213 a^{3} + 475 a^{2} - 379 a - 264\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+5a\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+3a^{3}-3a^{2}-2a-3\right){x}^{2}+\left(16a^{5}-79a^{4}+55a^{3}+179a^{2}-142a-103\right){x}+59a^{5}-278a^{4}+213a^{3}+475a^{2}-379a-264$ |
| 13.1-a1 |
13.1-a |
$2$ |
$7$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( -13 \) |
$143.55630$ |
$(a^4-3a^3-2a^2+7a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$0.110085406$ |
$6041.764842$ |
3.07602 |
\( -\frac{118442868691}{13} a^{5} + \frac{101668743464}{13} a^{4} + \frac{691493932735}{13} a^{3} - \frac{58803932310}{13} a^{2} - \frac{955012280447}{13} a - \frac{387148670317}{13} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( a^{2} - a - 1\) , \( a^{2} - a - 1\) , \( -205 a^{5} + 855 a^{4} - 159 a^{3} - 2512 a^{2} + 1434 a + 1266\) , \( -3465 a^{5} + 14362 a^{4} - 2541 a^{3} - 42203 a^{2} + 23921 a + 21276\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-205a^{5}+855a^{4}-159a^{3}-2512a^{2}+1434a+1266\right){x}-3465a^{5}+14362a^{4}-2541a^{3}-42203a^{2}+23921a+21276$ |
| 13.1-a2 |
13.1-a |
$2$ |
$7$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( - 13^{7} \) |
$143.55630$ |
$(a^4-3a^3-2a^2+7a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 7 \) |
$0.015726486$ |
$6041.764842$ |
3.07602 |
\( \frac{25865881895611}{62748517} a^{5} - \frac{118725561416347}{62748517} a^{4} + \frac{77869345731221}{62748517} a^{3} + \frac{230081136476730}{62748517} a^{2} - \frac{168021656253486}{62748517} a - \frac{123975562630979}{62748517} \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + 2 a^{2} + 10 a + 3\) , \( -a^{4} + 3 a^{3} + 4 a^{2} - 8 a - 7\) , \( a^{5} - a^{4} - 6 a^{3} + 2 a^{2} + 10 a + 4\) , \( 4 a^{5} - 3 a^{4} - 21 a^{3} + 2 a^{2} + 30 a + 14\) , \( 24 a^{5} - 29 a^{4} - 144 a^{3} + 61 a^{2} + 260 a + 99\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+2a^{2}+10a+3\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+2a^{2}+10a+4\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+4a^{2}-8a-7\right){x}^{2}+\left(4a^{5}-3a^{4}-21a^{3}+2a^{2}+30a+14\right){x}+24a^{5}-29a^{4}-144a^{3}+61a^{2}+260a+99$ |
| 13.1-b1 |
13.1-b |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( -13 \) |
$143.55630$ |
$(a^4-3a^3-2a^2+7a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.107860143$ |
$4881.199310$ |
2.43491 |
\( -\frac{9407062524507743}{13} a^{5} + \frac{38960838279392694}{13} a^{4} - \frac{6851713040159343}{13} a^{3} - \frac{114469497978376534}{13} a^{2} + \frac{64835611095003056}{13} a + \frac{57678763895055947}{13} \) |
\( \bigl[a^{3} - 3 a - 2\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 9 a^{2} - a - 6\) , \( a^{5} - a^{4} - 6 a^{3} + a^{2} + 11 a + 6\) , \( 11 a^{5} - 12 a^{4} - 62 a^{3} + 14 a^{2} + 93 a + 40\) , \( 6 a^{5} - 6 a^{4} - 32 a^{3} + 6 a^{2} + 41 a + 14\bigr] \) |
${y}^2+\left(a^{3}-3a-2\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+a^{2}+11a+6\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+9a^{2}-a-6\right){x}^{2}+\left(11a^{5}-12a^{4}-62a^{3}+14a^{2}+93a+40\right){x}+6a^{5}-6a^{4}-32a^{3}+6a^{2}+41a+14$ |
| 13.1-c1 |
13.1-c |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
13.1 |
\( 13 \) |
\( - 13^{3} \) |
$143.55630$ |
$(a^4-3a^3-2a^2+7a+2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.003580824$ |
$65809.68185$ |
3.26957 |
\( \frac{1964002694}{2197} a^{5} - \frac{6885655441}{2197} a^{4} - \frac{4398532653}{2197} a^{3} + \frac{27785301433}{2197} a^{2} - \frac{185764978}{2197} a - \frac{27464161628}{2197} \) |
\( \bigl[a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 6\) , \( -a^{5} + a^{4} + 6 a^{3} - a^{2} - 11 a - 5\) , \( a^{4} - a^{3} - 4 a^{2} + a + 3\) , \( -a^{5} + 7 a^{4} - 11 a^{3} - 12 a^{2} + 21 a + 10\) , \( a^{5} + 2 a^{4} - 16 a^{3} - 3 a^{2} + 30 a + 13\bigr] \) |
${y}^2+\left(a^{4}-2a^{3}-4a^{2}+6a+6\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+a+3\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-a^{2}-11a-5\right){x}^{2}+\left(-a^{5}+7a^{4}-11a^{3}-12a^{2}+21a+10\right){x}+a^{5}+2a^{4}-16a^{3}-3a^{2}+30a+13$ |
| 13.2-a1 |
13.2-a |
$2$ |
$7$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
13.2 |
\( 13 \) |
\( -13 \) |
$143.55630$ |
$(a^3-a^2-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 1 \) |
$0.110085406$ |
$6041.764842$ |
3.07602 |
\( \frac{118442868691}{13} a^{5} - \frac{490545599991}{13} a^{4} + \frac{86259780319}{13} a^{3} + \frac{1441261639769}{13} a^{2} - \frac{816322283539}{13} a - \frac{726245075566}{13} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + 2 a - 1\) , \( -a^{4} + 3 a^{3} + 3 a^{2} - 8 a - 6\) , \( a^{5} - a^{4} - 6 a^{3} + 2 a^{2} + 9 a + 3\) , \( 15 a^{5} - 13 a^{4} - 79 a^{3} + 11 a^{2} + 104 a + 39\) , \( 38 a^{5} - 25 a^{4} - 223 a^{3} + 9 a^{2} + 311 a + 128\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+2a-1\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+2a^{2}+9a+3\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+3a^{2}-8a-6\right){x}^{2}+\left(15a^{5}-13a^{4}-79a^{3}+11a^{2}+104a+39\right){x}+38a^{5}-25a^{4}-223a^{3}+9a^{2}+311a+128$ |
| 13.2-a2 |
13.2-a |
$2$ |
$7$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
13.2 |
\( 13 \) |
\( - 13^{7} \) |
$143.55630$ |
$(a^3-a^2-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1[3] |
$1$ |
\( 7 \) |
$0.015726486$ |
$6041.764842$ |
3.07602 |
\( -\frac{25865881895611}{62748517} a^{5} + \frac{10603848061708}{62748517} a^{4} + \frac{138374080978057}{62748517} a^{3} + \frac{9994624128421}{62748517} a^{2} - \frac{180175817706304}{62748517} a - \frac{76906416197250}{62748517} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 3 a^{2} + 2 a + 3\) , \( a + 1\) , \( -2 a^{5} + 8 a^{4} + 5 a^{3} - 33 a^{2} - a + 34\) , \( -18 a^{5} + 72 a^{4} + 28 a^{3} - 293 a^{2} + 30 a + 293\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-3a^{3}+3a^{2}+2a+3\right){x}^{2}+\left(-2a^{5}+8a^{4}+5a^{3}-33a^{2}-a+34\right){x}-18a^{5}+72a^{4}+28a^{3}-293a^{2}+30a+293$ |
| 13.2-b1 |
13.2-b |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
13.2 |
\( 13 \) |
\( -13 \) |
$143.55630$ |
$(a^3-a^2-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.107860143$ |
$4881.199310$ |
2.43491 |
\( \frac{9407062524507743}{13} a^{5} - \frac{8074474343146021}{13} a^{4} - \frac{54921014832334003}{13} a^{3} + \frac{4669767332424171}{13} a^{2} + \frac{75850483487195980}{13} a + \frac{30746939726408077}{13} \) |
\( \bigl[a^{3} - a^{2} - 2 a\) , \( a^{5} - a^{4} - 7 a^{3} + 3 a^{2} + 11 a + 2\) , \( a^{5} - a^{4} - 5 a^{3} + 8 a + 6\) , \( -12 a^{5} + 44 a^{4} + a^{3} - 129 a^{2} + 62 a + 74\) , \( -18 a^{5} + 74 a^{4} - 15 a^{3} - 214 a^{2} + 127 a + 105\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+8a+6\right){y}={x}^{3}+\left(a^{5}-a^{4}-7a^{3}+3a^{2}+11a+2\right){x}^{2}+\left(-12a^{5}+44a^{4}+a^{3}-129a^{2}+62a+74\right){x}-18a^{5}+74a^{4}-15a^{3}-214a^{2}+127a+105$ |
| 13.2-c1 |
13.2-c |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
13.2 |
\( 13 \) |
\( - 13^{3} \) |
$143.55630$ |
$(a^3-a^2-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.003580824$ |
$65809.68185$ |
3.26957 |
\( -\frac{1964002694}{2197} a^{5} + \frac{2934358029}{2197} a^{4} + \frac{12301127477}{2197} a^{3} - \frac{7084202232}{2197} a^{2} - \frac{24466631635}{2197} a - \frac{9184810573}{2197} \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + 2 a^{2} + 10 a + 3\) , \( a - 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( -33 a^{5} + 141 a^{4} - 32 a^{3} - 415 a^{2} + 246 a + 213\) , \( 74 a^{5} - 297 a^{4} + 38 a^{3} + 867 a^{2} - 472 a - 425\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+2a^{2}+10a+3\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-33a^{5}+141a^{4}-32a^{3}-415a^{2}+246a+213\right){x}+74a^{5}-297a^{4}+38a^{3}+867a^{2}-472a-425$ |
| 29.1-a1 |
29.1-a |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
29.1 |
\( 29 \) |
\( 29^{4} \) |
$153.48295$ |
$(-a^4+2a^3+4a^2-4a-6)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.003379084$ |
$57946.80409$ |
3.62230 |
\( \frac{151764642}{707281} a^{5} + \frac{1199291385}{707281} a^{4} - \frac{2853486585}{707281} a^{3} - \frac{4625385057}{707281} a^{2} + \frac{3632328483}{707281} a + \frac{3617442046}{707281} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + 3 a\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + 2 a - 2\) , \( a^{5} + 6 a^{4} - 12 a^{3} - 31 a^{2} + 21 a + 41\) , \( 8 a^{5} - 11 a^{4} - 34 a^{3} + 31 a^{2} + 36 a - 14\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+a-1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+2a-2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}+3a\right){x}^{2}+\left(a^{5}+6a^{4}-12a^{3}-31a^{2}+21a+41\right){x}+8a^{5}-11a^{4}-34a^{3}+31a^{2}+36a-14$ |
| 29.2-a1 |
29.2-a |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
29.2 |
\( 29 \) |
\( 29^{4} \) |
$153.48295$ |
$(a^4-2a^3-4a^2+6a+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.003379084$ |
$57946.80409$ |
3.62230 |
\( -\frac{151764642}{707281} a^{5} + \frac{1958114595}{707281} a^{4} - \frac{3461325375}{707281} a^{3} - \frac{4472450082}{707281} a^{2} + \frac{8622912636}{707281} a + \frac{1121954914}{707281} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 7 a + 5\) , \( -a^{5} + a^{4} + 7 a^{3} - 2 a^{2} - 13 a - 5\) , \( 1\) , \( -2 a^{4} - 3 a^{3} + 11 a^{2} + 21 a + 7\) , \( -13 a^{5} + 17 a^{4} + 80 a^{3} - 35 a^{2} - 146 a - 56\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+7a+5\right){x}{y}+{y}={x}^{3}+\left(-a^{5}+a^{4}+7a^{3}-2a^{2}-13a-5\right){x}^{2}+\left(-2a^{4}-3a^{3}+11a^{2}+21a+7\right){x}-13a^{5}+17a^{4}+80a^{3}-35a^{2}-146a-56$ |
| 41.1-a1 |
41.1-a |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
41.1 |
\( 41 \) |
\( 41^{2} \) |
$157.97643$ |
$(a^4-a^3-6a^2+3a+6)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.000909628$ |
$95412.04423$ |
4.81664 |
\( \frac{1831916}{1681} a^{5} - \frac{543881}{1681} a^{4} - \frac{12753285}{1681} a^{3} + \frac{745703}{1681} a^{2} + \frac{16545361}{1681} a + \frac{4112871}{1681} \) |
\( \bigl[a^{3} - 3 a - 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 6 a^{2} + 9 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 6 a^{5} - 7 a^{4} - 35 a^{3} + 14 a^{2} + 61 a + 23\) , \( 8 a^{5} - 8 a^{4} - 47 a^{3} + 14 a^{2} + 81 a + 33\bigr] \) |
${y}^2+\left(a^{3}-3a-2\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+6a^{2}+9a+1\right){x}^{2}+\left(6a^{5}-7a^{4}-35a^{3}+14a^{2}+61a+23\right){x}+8a^{5}-8a^{4}-47a^{3}+14a^{2}+81a+33$ |
| 41.2-a1 |
41.2-a |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
41.2 |
\( 41 \) |
\( 41^{2} \) |
$157.97643$ |
$(-a^5+7a^3+a^2-11a-4)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.000909628$ |
$95412.04423$ |
4.81664 |
\( -\frac{1831916}{1681} a^{5} + \frac{210139}{41} a^{4} - \frac{3390351}{1681} a^{3} - \frac{22458278}{1681} a^{2} + \frac{13239032}{1681} a + \frac{9938685}{1681} \) |
\( \bigl[a^{3} - a^{2} - 2 a\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 9 a^{2} - 4\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 3\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a\right){x}{y}+\left(a^{4}-a^{3}-4a^{2}+2a+3\right){y}={x}^{3}+\left(a^{5}-3a^{4}-2a^{3}+9a^{2}-4\right){x}^{2}$ |
| 43.1-a1 |
43.1-a |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
43.1 |
\( 43 \) |
\( 43^{6} \) |
$158.60469$ |
$(a^5-3a^4-2a^3+8a^2+a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1431.168640$ |
2.20631 |
\( \frac{1545053960593002}{6321363049} a^{5} - \frac{5385447961550674}{6321363049} a^{4} - \frac{3504729616418335}{6321363049} a^{3} + \frac{21722107126780968}{6321363049} a^{2} - \frac{58735384383778}{6321363049} a - \frac{21448949004140755}{6321363049} \) |
\( \bigl[a^{3} - 3 a - 2\) , \( a^{4} - a^{3} - 6 a^{2} + 3 a + 8\) , \( 1\) , \( 6 a^{5} - 13 a^{4} - 21 a^{3} + 44 a^{2} + 18 a - 31\) , \( 12 a^{5} - 28 a^{4} - 54 a^{3} + 131 a^{2} + 61 a - 153\bigr] \) |
${y}^2+\left(a^{3}-3a-2\right){x}{y}+{y}={x}^{3}+\left(a^{4}-a^{3}-6a^{2}+3a+8\right){x}^{2}+\left(6a^{5}-13a^{4}-21a^{3}+44a^{2}+18a-31\right){x}+12a^{5}-28a^{4}-54a^{3}+131a^{2}+61a-153$ |
| 43.1-b1 |
43.1-b |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
43.1 |
\( 43 \) |
\( 43^{4} \) |
$158.60469$ |
$(a^5-3a^4-2a^3+8a^2+a-3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.025703319$ |
$7960.994389$ |
3.78541 |
\( -\frac{6862418975964}{3418801} a^{5} + \frac{30848750157018}{3418801} a^{4} - \frac{18712098139415}{3418801} a^{3} - \frac{61009164594246}{3418801} a^{2} + \frac{42761979884482}{3418801} a + \frac{32262339489542}{3418801} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 6 a + 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 4 a^{2} + 7 a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + 2 a - 1\) , \( -4 a^{5} + 22 a^{4} - 11 a^{3} - 98 a^{2} + 64 a + 138\) , \( -42 a^{5} + 155 a^{4} + 69 a^{3} - 639 a^{2} + 90 a + 692\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+6a+1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+2a-1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+4a^{2}+7a+3\right){x}^{2}+\left(-4a^{5}+22a^{4}-11a^{3}-98a^{2}+64a+138\right){x}-42a^{5}+155a^{4}+69a^{3}-639a^{2}+90a+692$ |
| 43.2-a1 |
43.2-a |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
43.2 |
\( 43 \) |
\( 43^{6} \) |
$158.60469$ |
$(a^5-2a^4-4a^3+6a^2+4a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$1431.168640$ |
2.20631 |
\( -\frac{1545053960593002}{6321363049} a^{5} + \frac{2339821841414336}{6321363049} a^{4} + \frac{9595981856691011}{6321363049} a^{3} - \frac{5654229885848061}{6321363049} a^{2} - \frac{19054767976685467}{6321363049} a - \frac{7130700879119572}{6321363049} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + 3 a\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 5 a - 1\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 5 a + 5\) , \( -4 a^{5} + 4 a^{4} + 24 a^{3} - 4 a^{2} - 34 a - 12\) , \( 196 a^{5} - 168 a^{4} - 1144 a^{3} + 97 a^{2} + 1579 a + 639\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}+3a\right){x}{y}+\left(a^{4}-2a^{3}-4a^{2}+5a+5\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+5a-1\right){x}^{2}+\left(-4a^{5}+4a^{4}+24a^{3}-4a^{2}-34a-12\right){x}+196a^{5}-168a^{4}-1144a^{3}+97a^{2}+1579a+639$ |
| 43.2-b1 |
43.2-b |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
43.2 |
\( 43 \) |
\( 43^{4} \) |
$158.60469$ |
$(a^5-2a^4-4a^3+6a^2+4a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.025703319$ |
$7960.994389$ |
3.78541 |
\( \frac{6862418975964}{3418801} a^{5} - \frac{3463344722802}{3418801} a^{4} - \frac{36058712729017}{3418801} a^{3} - \frac{677147830023}{3418801} a^{2} + \frac{46309737974003}{3418801} a + \frac{19289387821417}{3418801} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 3 a + 6\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 4 a - 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 5 a\) , \( 7 a^{5} - 17 a^{4} - 11 a^{3} + 30 a^{2} + 6 a - 2\) , \( 8 a^{5} - 14 a^{4} - 25 a^{3} + 26 a^{2} + 25 a + 4\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+6\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+5a\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+4a-1\right){x}^{2}+\left(7a^{5}-17a^{4}-11a^{3}+30a^{2}+6a-2\right){x}+8a^{5}-14a^{4}-25a^{3}+26a^{2}+25a+4$ |
| 49.1-a1 |
49.1-a |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{3} \) |
$160.34053$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.078573988$ |
$17929.06718$ |
3.25763 |
\( -6163690618880 a^{5} + 5290547871744 a^{4} + 35985318346756 a^{3} - 3059699482634 a^{2} - 49698692005891 a - 20145988041971 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{4} - a^{3} - 4 a^{2} + a + 4\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 5\) , \( -13 a^{5} + 66 a^{4} - 36 a^{3} - 190 a^{2} + 157 a + 81\) , \( -98 a^{5} + 420 a^{4} - 112 a^{3} - 1204 a^{2} + 786 a + 525\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{4}-2a^{3}-4a^{2}+6a+5\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+a+4\right){x}^{2}+\left(-13a^{5}+66a^{4}-36a^{3}-190a^{2}+157a+81\right){x}-98a^{5}+420a^{4}-112a^{3}-1204a^{2}+786a+525$ |
| 49.1-a2 |
49.1-a |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{3} \) |
$160.34053$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.039286994$ |
$35858.13437$ |
3.25763 |
\( -905248 a^{5} + 778380 a^{4} + 5283988 a^{3} - 455499 a^{2} - 7299070 a - 2955639 \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + a^{2} + 11 a + 6\) , \( a^{4} - a^{3} - 4 a^{2} + 2\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 6 a\) , \( -a^{4} + a^{3} + 8 a^{2} - 3 a - 11\) , \( 6 a^{5} - 20 a^{4} - a^{3} + 40 a^{2} - 6 a - 15\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+a^{2}+11a+6\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+6a\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+2\right){x}^{2}+\left(-a^{4}+a^{3}+8a^{2}-3a-11\right){x}+6a^{5}-20a^{4}-a^{3}+40a^{2}-6a-15$ |
| 49.1-b1 |
49.1-b |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{11} \) |
$160.34053$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.406525840$ |
$4907.397794$ |
4.61324 |
\( \frac{20910}{49} a^{5} + \frac{324350}{49} a^{4} - \frac{61827}{7} a^{3} - \frac{1575082}{49} a^{2} + \frac{890287}{49} a + \frac{274095}{7} \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + 2 a^{2} + 10 a + 3\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 3 a^{2} - 2 a - 2\) , \( a^{5} - a^{4} - 6 a^{3} + a^{2} + 10 a + 6\) , \( 4 a^{5} - 16 a^{4} + a^{3} + 54 a^{2} - 23 a - 38\) , \( -25 a^{5} + 105 a^{4} - 14 a^{3} - 321 a^{2} + 164 a + 186\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+2a^{2}+10a+3\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+a^{2}+10a+6\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+3a^{3}-3a^{2}-2a-2\right){x}^{2}+\left(4a^{5}-16a^{4}+a^{3}+54a^{2}-23a-38\right){x}-25a^{5}+105a^{4}-14a^{3}-321a^{2}+164a+186$ |
| 49.1-b2 |
49.1-b |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{16} \) |
$160.34053$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.813051680$ |
$1226.849448$ |
4.61324 |
\( \frac{207225358689}{2401} a^{5} + \frac{260903631341}{2401} a^{4} - \frac{1440312844568}{2401} a^{3} - \frac{1737027620152}{2401} a^{2} + \frac{313731722981}{343} a + \frac{369533528708}{343} \) |
\( \bigl[a^{4} - a^{3} - 5 a^{2} + 2 a + 6\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 4 a^{2} - 5 a - 3\) , \( a^{4} - a^{3} - 5 a^{2} + 2 a + 5\) , \( -74 a^{5} + 83 a^{4} + 542 a^{3} - 216 a^{2} - 1078 a - 430\) , \( 721 a^{5} - 1209 a^{4} - 4129 a^{3} + 2831 a^{2} + 8196 a + 2975\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+2a+6\right){x}{y}+\left(a^{4}-a^{3}-5a^{2}+2a+5\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-4a^{2}-5a-3\right){x}^{2}+\left(-74a^{5}+83a^{4}+542a^{3}-216a^{2}-1078a-430\right){x}+721a^{5}-1209a^{4}-4129a^{3}+2831a^{2}+8196a+2975$ |
| 49.1-c1 |
49.1-c |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{9} \) |
$160.34053$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.206022754$ |
$9247.746300$ |
4.40572 |
\( -6163690618880 a^{5} + 5290547871744 a^{4} + 35985318346756 a^{3} - 3059699482634 a^{2} - 49698692005891 a - 20145988041971 \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 4 a + 2\) , \( a^{5} - a^{4} - 6 a^{3} + 2 a^{2} + 9 a + 3\) , \( 4 a^{5} - 22 a^{4} + 28 a^{3} + 27 a^{2} - 39 a - 34\) , \( -31 a^{5} + 143 a^{4} - 116 a^{3} - 190 a^{2} + 155 a + 65\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+2a^{2}+9a+3\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-4a+2\right){x}^{2}+\left(4a^{5}-22a^{4}+28a^{3}+27a^{2}-39a-34\right){x}-31a^{5}+143a^{4}-116a^{3}-190a^{2}+155a+65$ |
| 49.1-c2 |
49.1-c |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.1 |
\( 7^{2} \) |
\( - 7^{9} \) |
$160.34053$ |
$(-a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.103011377$ |
$18495.49260$ |
4.40572 |
\( -905248 a^{5} + 778380 a^{4} + 5283988 a^{3} - 455499 a^{2} - 7299070 a - 2955639 \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 4 a + 2\) , \( a^{5} - a^{4} - 6 a^{3} + 2 a^{2} + 9 a + 3\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 8 a^{2} - 4 a + 1\) , \( -a^{5} + 8 a^{4} - 10 a^{3} - 15 a^{2} + 15 a + 9\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+2a^{2}+9a+3\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-4a+2\right){x}^{2}+\left(-a^{5}+3a^{4}+3a^{3}-8a^{2}-4a+1\right){x}-a^{5}+8a^{4}-10a^{3}-15a^{2}+15a+9$ |
| 49.2-a1 |
49.2-a |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{5} \) |
$160.34053$ |
$(-a), (-a^5+3a^4+2a^3-9a^2+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4208.057509$ |
1.62180 |
\( -\frac{45707260}{49} a^{5} + \frac{156861776}{49} a^{4} + \frac{119581507}{49} a^{3} - \frac{94967674}{7} a^{2} - \frac{2348652}{7} a + \frac{95634941}{7} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 7 a + 3\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 6\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 6\) , \( 4 a^{5} - a^{4} - 27 a^{3} + 6 a^{2} + 39 a - 6\) , \( -4 a^{5} + 40 a^{4} - 31 a^{3} - 146 a^{2} + 89 a + 122\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+a^{2}+7a+3\right){x}{y}+\left(a^{4}-2a^{3}-4a^{2}+6a+6\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-7a-6\right){x}^{2}+\left(4a^{5}-a^{4}-27a^{3}+6a^{2}+39a-6\right){x}-4a^{5}+40a^{4}-31a^{3}-146a^{2}+89a+122$ |
| 49.2-a2 |
49.2-a |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{10} \) |
$160.34053$ |
$(-a), (-a^5+3a^4+2a^3-9a^2+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$526.0071887$ |
1.62180 |
\( -\frac{28136858361347}{343} a^{5} + \frac{127011699532204}{343} a^{4} - \frac{79683575114636}{343} a^{3} - \frac{5007387686670}{7} a^{2} + \frac{24920965515519}{49} a + \frac{18602846309807}{49} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 7 a + 3\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 6\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 6\) , \( -31 a^{5} + 139 a^{4} - 42 a^{3} - 404 a^{2} + 259 a + 194\) , \( -277 a^{5} + 1162 a^{4} - 211 a^{3} - 3441 a^{2} + 1935 a + 1769\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+a^{2}+7a+3\right){x}{y}+\left(a^{4}-2a^{3}-4a^{2}+6a+6\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-7a-6\right){x}^{2}+\left(-31a^{5}+139a^{4}-42a^{3}-404a^{2}+259a+194\right){x}-277a^{5}+1162a^{4}-211a^{3}-3441a^{2}+1935a+1769$ |
| 49.2-b1 |
49.2-b |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( - 7^{5} \) |
$160.34053$ |
$(-a), (-a^5+3a^4+2a^3-9a^2+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4208.057509$ |
1.62180 |
\( \frac{45707260}{49} a^{5} - \frac{71674524}{49} a^{4} - \frac{289956011}{49} a^{3} + \frac{178068859}{49} a^{2} + \frac{84047525}{7} a + \frac{31280904}{7} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 5 a\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 5 a - 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 6 a\) , \( -4 a^{5} + 5 a^{4} + 27 a^{3} - 15 a^{2} - 50 a - 14\) , \( 5 a^{4} - 17 a^{3} - 6 a^{2} + 35 a + 14\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+5a\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+6a\right){y}={x}^{3}+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+5a-4\right){x}^{2}+\left(-4a^{5}+5a^{4}+27a^{3}-15a^{2}-50a-14\right){x}+5a^{4}-17a^{3}-6a^{2}+35a+14$ |
| 49.2-b2 |
49.2-b |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{10} \) |
$160.34053$ |
$(-a), (-a^5+3a^4+2a^3-9a^2+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$526.0071887$ |
1.62180 |
\( \frac{28136858361347}{343} a^{5} - \frac{13672592274531}{343} a^{4} - \frac{146994639400710}{343} a^{3} - \frac{3711108410984}{343} a^{2} + \frac{187965453706854}{343} a + \frac{11213707455239}{49} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 5 a\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 5 a - 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 6 a\) , \( -9 a^{5} + 10 a^{4} + 47 a^{3} - 20 a^{2} - 75 a - 24\) , \( -20 a^{5} + 21 a^{4} + 81 a^{3} - 23 a^{2} - 100 a - 38\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+5a\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+6a\right){y}={x}^{3}+\left(a^{5}-3a^{4}-3a^{3}+9a^{2}+5a-4\right){x}^{2}+\left(-9a^{5}+10a^{4}+47a^{3}-20a^{2}-75a-24\right){x}-20a^{5}+21a^{4}+81a^{3}-23a^{2}-100a-38$ |
| 49.2-c1 |
49.2-c |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{2} \) |
$160.34053$ |
$(-a), (-a^5+3a^4+2a^3-9a^2+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.019434397$ |
$43252.62462$ |
3.88758 |
\( 4096 a^{5} - \frac{176128}{7} a^{4} + \frac{237568}{7} a^{3} + \frac{311296}{7} a^{2} - 73728 a - 40960 \) |
\( \bigl[0\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + 3 a - 4\) , \( a^{5} - a^{4} - 5 a^{3} + 7 a + 5\) , \( -a^{5} + 5 a^{4} - 24 a^{2} + 8 a + 33\) , \( a^{5} - a^{4} - 6 a^{3} + 10 a + 7\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+7a+5\right){y}={x}^{3}+\left(a^{5}-3a^{4}-3a^{3}+10a^{2}+3a-4\right){x}^{2}+\left(-a^{5}+5a^{4}-24a^{2}+8a+33\right){x}+a^{5}-a^{4}-6a^{3}+10a+7$ |
| 49.2-d1 |
49.2-d |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{2} \) |
$160.34053$ |
$(-a), (-a^5+3a^4+2a^3-9a^2+5)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.019434397$ |
$43252.62462$ |
3.88758 |
\( -4096 a^{5} - \frac{32768}{7} a^{4} + \frac{180224}{7} a^{3} + \frac{253952}{7} a^{2} - 36864 a - 57344 \) |
\( \bigl[0\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 10 a^{2} + 2 a + 7\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 5\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 5 a + 1\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 5 a^{2} - a + 1\bigr] \) |
${y}^2+\left(a^{4}-a^{3}-5a^{2}+3a+5\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+2a^{3}-10a^{2}+2a+7\right){x}^{2}+\left(-a^{4}+2a^{3}+3a^{2}-5a+1\right){x}-a^{5}+2a^{4}+3a^{3}-5a^{2}-a+1$ |
| 49.3-a1 |
49.3-a |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{3} \) |
$160.34053$ |
$(-a^5+3a^4+2a^3-9a^2+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.078573988$ |
$17929.06718$ |
3.25763 |
\( 6163690618880 a^{5} - 25527905222656 a^{4} + 4489396355068 a^{3} + 75002636599298 a^{2} - 42481602461685 a - 37792203930876 \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 6 a\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 3 a - 2\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 6 a + 1\) , \( -22 a^{5} + 17 a^{4} + 128 a^{3} - 17 a^{2} - 210 a - 96\) , \( -140 a^{5} + 120 a^{4} + 775 a^{3} - 178 a^{2} - 1195 a - 454\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+6a\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+6a+1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+3a-2\right){x}^{2}+\left(-22a^{5}+17a^{4}+128a^{3}-17a^{2}-210a-96\right){x}-140a^{5}+120a^{4}+775a^{3}-178a^{2}-1195a-454$ |
| 49.3-a2 |
49.3-a |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.3 |
\( 7^{2} \) |
\( - 7^{3} \) |
$160.34053$ |
$(-a^5+3a^4+2a^3-9a^2+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.039286994$ |
$35858.13437$ |
3.25763 |
\( 905248 a^{5} - 3747860 a^{4} + 654972 a^{3} + 11014265 a^{2} - 6229176 a - 5553088 \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 6 a\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 3 a - 2\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 6 a + 1\) , \( -2 a^{5} + 2 a^{4} + 13 a^{3} - 2 a^{2} - 25 a - 11\) , \( -5 a^{5} + 4 a^{4} + 27 a^{3} - 5 a^{2} - 41 a - 16\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+6a\right){x}{y}+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+6a+1\right){y}={x}^{3}+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+3a-2\right){x}^{2}+\left(-2a^{5}+2a^{4}+13a^{3}-2a^{2}-25a-11\right){x}-5a^{5}+4a^{4}+27a^{3}-5a^{2}-41a-16$ |
| 49.3-b1 |
49.3-b |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.3 |
\( 7^{2} \) |
\( - 7^{11} \) |
$160.34053$ |
$(-a^5+3a^4+2a^3-9a^2+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.406525840$ |
$4907.397794$ |
4.61324 |
\( -\frac{20910}{49} a^{5} + \frac{428900}{49} a^{4} - \frac{1073711}{49} a^{3} - \frac{102607}{7} a^{2} + 44006 a + \frac{163763}{7} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 6 a\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( -5 a^{5} + 7 a^{4} + 26 a^{3} - 14 a^{2} - 38 a - 11\) , \( 22 a^{5} - 19 a^{4} - 132 a^{3} + 13 a^{2} + 194 a + 80\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-1\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+a-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-5a^{2}-6a\right){x}^{2}+\left(-5a^{5}+7a^{4}+26a^{3}-14a^{2}-38a-11\right){x}+22a^{5}-19a^{4}-132a^{3}+13a^{2}+194a+80$ |
| 49.3-b2 |
49.3-b |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.3 |
\( 7^{2} \) |
\( - 7^{16} \) |
$160.34053$ |
$(-a^5+3a^4+2a^3-9a^2+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.813051680$ |
$1226.849448$ |
4.61324 |
\( -\frac{207225358689}{2401} a^{5} + \frac{1297030424786}{2401} a^{4} - \frac{1675555267686}{2401} a^{3} - \frac{345755825560}{343} a^{2} + \frac{502732913476}{343} a + \frac{296235041019}{343} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + 2 a + 1\) , \( a^{4} - a^{3} - 4 a^{2} + 4\) , \( a^{5} - a^{4} - 5 a^{3} + a^{2} + 6 a + 4\) , \( 867 a^{5} - 3029 a^{4} - 1955 a^{3} + 12211 a^{2} - 52 a - 12052\) , \( -19164 a^{5} + 67106 a^{4} + 42999 a^{3} - 270718 a^{2} + 1619 a + 267517\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}+2a+1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+a^{2}+6a+4\right){y}={x}^{3}+\left(a^{4}-a^{3}-4a^{2}+4\right){x}^{2}+\left(867a^{5}-3029a^{4}-1955a^{3}+12211a^{2}-52a-12052\right){x}-19164a^{5}+67106a^{4}+42999a^{3}-270718a^{2}+1619a+267517$ |
| 49.3-c1 |
49.3-c |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.3 |
\( 7^{2} \) |
\( 7^{9} \) |
$160.34053$ |
$(-a^5+3a^4+2a^3-9a^2+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.206022754$ |
$9247.746300$ |
4.40572 |
\( 6163690618880 a^{5} - 25527905222656 a^{4} + 4489396355068 a^{3} + 75002636599298 a^{2} - 42481602461685 a - 37792203930876 \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + 2 a^{2} + 10 a + 3\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 4 a^{2} - 2 a + 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( -4 a^{5} - 2 a^{4} + 18 a^{3} + 17 a^{2} - 19 a - 25\) , \( 18 a^{5} - 11 a^{4} - 78 a^{3} + 16 a^{2} + 69 a - 2\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+2a^{2}+10a+3\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+a-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+3a^{3}-4a^{2}-2a+1\right){x}^{2}+\left(-4a^{5}-2a^{4}+18a^{3}+17a^{2}-19a-25\right){x}+18a^{5}-11a^{4}-78a^{3}+16a^{2}+69a-2$ |
| 49.3-c2 |
49.3-c |
$2$ |
$2$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
49.3 |
\( 7^{2} \) |
\( - 7^{9} \) |
$160.34053$ |
$(-a^5+3a^4+2a^3-9a^2+5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.103011377$ |
$18495.49260$ |
4.40572 |
\( 905248 a^{5} - 3747860 a^{4} + 654972 a^{3} + 11014265 a^{2} - 6229176 a - 5553088 \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + 2 a^{2} + 10 a + 3\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 4 a^{2} - 2 a + 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( a^{5} - 2 a^{4} - 7 a^{3} + 7 a^{2} + 16 a + 5\) , \( 3 a^{5} - a^{4} - 19 a^{3} - a^{2} + 31 a + 13\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+2a^{2}+10a+3\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+a-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+3a^{3}-4a^{2}-2a+1\right){x}^{2}+\left(a^{5}-2a^{4}-7a^{3}+7a^{2}+16a+5\right){x}+3a^{5}-a^{4}-19a^{3}-a^{2}+31a+13$ |
| 71.1-a1 |
71.1-a |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( -71 \) |
$165.37322$ |
$(-a^5+4a^4-13a^2+5a+11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.043419546$ |
$16136.44718$ |
3.24033 |
\( -\frac{3750585}{71} a^{5} + \frac{2084821}{71} a^{4} + \frac{19162527}{71} a^{3} - \frac{279653}{71} a^{2} - \frac{24191375}{71} a - \frac{9895665}{71} \) |
\( \bigl[1\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 8\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -2 a^{3} + 7 a + 6\) , \( a^{3} - 4 a - 3\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-7a-8\right){x}^{2}+\left(-2a^{3}+7a+6\right){x}+a^{3}-4a-3$ |
| 71.1-b1 |
71.1-b |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( 71^{2} \) |
$165.37322$ |
$(-a^5+4a^4-13a^2+5a+11)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.031027105$ |
$17568.15058$ |
5.04189 |
\( -\frac{410245}{5041} a^{5} + \frac{4835943}{5041} a^{4} - \frac{9124038}{5041} a^{3} - \frac{5733537}{5041} a^{2} + \frac{12614143}{5041} a + \frac{6289578}{5041} \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + a^{2} + 11 a + 6\) , \( -a^{5} + a^{4} + 5 a^{3} - a^{2} - 7 a - 4\) , \( a^{5} - a^{4} - 5 a^{3} + a^{2} + 7 a + 4\) , \( 2 a^{5} - 7 a^{4} - 6 a^{3} + 18 a^{2} + 15 a + 2\) , \( 3 a^{5} - 8 a^{4} - 13 a^{3} + 19 a^{2} + 30 a + 9\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+a^{2}+11a+6\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+a^{2}+7a+4\right){y}={x}^{3}+\left(-a^{5}+a^{4}+5a^{3}-a^{2}-7a-4\right){x}^{2}+\left(2a^{5}-7a^{4}-6a^{3}+18a^{2}+15a+2\right){x}+3a^{5}-8a^{4}-13a^{3}+19a^{2}+30a+9$ |
| 71.1-c1 |
71.1-c |
$2$ |
$3$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( - 71^{3} \) |
$165.37322$ |
$(-a^5+4a^4-13a^2+5a+11)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$34.24063407$ |
2.13783 |
\( -\frac{18074622308423149102843876}{357911} a^{5} + \frac{15514202622576919559212864}{357911} a^{4} + \frac{105524609547265110592704133}{357911} a^{3} - \frac{8972437525185746589511058}{357911} a^{2} - \frac{145738251166175872237887518}{357911} a - \frac{59076818214318159735089897}{357911} \) |
\( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + 2 a\) , \( -a^{4} + 3 a^{3} + 3 a^{2} - 8 a - 5\) , \( a^{2} - 2\) , \( 39 a^{5} - 138 a^{4} - 23 a^{3} + 403 a^{2} - 164 a - 176\) , \( 1047 a^{5} - 4226 a^{4} + 542 a^{3} + 12347 a^{2} - 6713 a - 6104\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-3a^{3}+4a^{2}+2a\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{4}+3a^{3}+3a^{2}-8a-5\right){x}^{2}+\left(39a^{5}-138a^{4}-23a^{3}+403a^{2}-164a-176\right){x}+1047a^{5}-4226a^{4}+542a^{3}+12347a^{2}-6713a-6104$ |
| 71.1-c2 |
71.1-c |
$2$ |
$3$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
71.1 |
\( 71 \) |
\( -71 \) |
$165.37322$ |
$(-a^5+4a^4-13a^2+5a+11)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$24961.42223$ |
2.13783 |
\( -\frac{82342970}{71} a^{5} + \frac{116854759}{71} a^{4} + \frac{388427705}{71} a^{3} - \frac{205288816}{71} a^{2} - \frac{453345905}{71} a - \frac{136787291}{71} \) |
\( \bigl[a^{3} - 4 a - 2\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 10 a^{2} - 2 a + 5\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 4\) , \( a^{5} - 8 a^{3} - a^{2} + 15 a + 5\) , \( 2 a^{5} - 6 a^{4} - 2 a^{3} + 14 a^{2} - 5 a - 2\bigr] \) |
${y}^2+\left(a^{3}-4a-2\right){x}{y}+\left(a^{4}-2a^{3}-3a^{2}+4a+4\right){y}={x}^{3}+\left(-a^{5}+3a^{4}+3a^{3}-10a^{2}-2a+5\right){x}^{2}+\left(a^{5}-8a^{3}-a^{2}+15a+5\right){x}+2a^{5}-6a^{4}-2a^{3}+14a^{2}-5a-2$ |
| 71.2-a1 |
71.2-a |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( 71^{2} \) |
$165.37322$ |
$(a^4-3a^3-2a^2+7a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.021395094$ |
$24770.40081$ |
4.90201 |
\( -\frac{110759401}{5041} a^{5} + \frac{374891300}{5041} a^{4} + \frac{3622381}{5041} a^{3} - \frac{537454969}{5041} a^{2} - \frac{99985379}{5041} a - \frac{252787413}{5041} \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + a^{2} + 11 a + 5\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 3 a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + a - 1\) , \( 4 a^{5} - 14 a^{4} - 7 a^{3} + 38 a^{2} + 10 a - 2\) , \( -2 a^{5} + 12 a^{4} - 16 a^{3} - 30 a^{2} + 51 a + 31\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+a^{2}+11a+5\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+a-1\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+4a^{3}-6a^{2}-3a+3\right){x}^{2}+\left(4a^{5}-14a^{4}-7a^{3}+38a^{2}+10a-2\right){x}-2a^{5}+12a^{4}-16a^{3}-30a^{2}+51a+31$ |
| 71.2-b1 |
71.2-b |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
71.2 |
\( 71 \) |
\( 71^{2} \) |
$165.37322$ |
$(a^4-3a^3-2a^2+7a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.402753357$ |
$1062.486483$ |
3.95812 |
\( -\frac{66473486525648211105901}{5041} a^{5} + \frac{275310465052630184206358}{5041} a^{4} - \frac{48416522512805062723541}{5041} a^{3} - \frac{808880201611245146201308}{5041} a^{2} + \frac{458150364076403387704378}{5041} a + \frac{407577660356242175733549}{5041} \) |
\( \bigl[a^{5} - a^{4} - 5 a^{3} + 8 a + 6\) , \( -a^{3} + 4 a + 2\) , \( a^{5} - a^{4} - 5 a^{3} + 8 a + 5\) , \( -3 a^{5} + 11 a^{3} + 30 a^{2} + 6 a - 75\) , \( -152 a^{5} + 438 a^{4} + 420 a^{3} - 1536 a^{2} - 175 a + 1254\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-5a^{3}+8a+6\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+8a+5\right){y}={x}^{3}+\left(-a^{3}+4a+2\right){x}^{2}+\left(-3a^{5}+11a^{3}+30a^{2}+6a-75\right){x}-152a^{5}+438a^{4}+420a^{3}-1536a^{2}-175a+1254$ |
| 71.3-a1 |
71.3-a |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
71.3 |
\( 71 \) |
\( 71^{2} \) |
$165.37322$ |
$(a^4-a^3-5a^2+2a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.021395094$ |
$24770.40081$ |
4.90201 |
\( \frac{110759401}{5041} a^{5} - \frac{178905705}{5041} a^{4} - \frac{395593571}{5041} a^{3} + \frac{615165964}{5041} a^{2} + \frac{218259979}{5041} a - \frac{622473481}{5041} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 4 a - 1\) , \( -a^{5} + a^{4} + 7 a^{3} - 3 a^{2} - 12 a - 4\) , \( 0\) , \( 6 a^{5} - 20 a^{4} - 17 a^{3} + 80 a^{2} + 11 a - 71\) , \( -15 a^{5} + 51 a^{4} + 37 a^{3} - 204 a^{2} - 9 a + 195\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+4a-1\right){x}{y}={x}^{3}+\left(-a^{5}+a^{4}+7a^{3}-3a^{2}-12a-4\right){x}^{2}+\left(6a^{5}-20a^{4}-17a^{3}+80a^{2}+11a-71\right){x}-15a^{5}+51a^{4}+37a^{3}-204a^{2}-9a+195$ |
| 71.3-b1 |
71.3-b |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
71.3 |
\( 71 \) |
\( 71^{2} \) |
$165.37322$ |
$(a^4-a^3-5a^2+2a+4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.402753357$ |
$1062.486483$ |
3.95812 |
\( \frac{66473486525648211105901}{5041} a^{5} - \frac{57056967575610871323147}{5041} a^{4} - \frac{388090472441233563042881}{5041} a^{3} + \frac{32998155909638659807207}{5041} a^{2} + \frac{535985179102222411572934}{5041} a + \frac{217268278835577327613535}{5041} \) |
\( \bigl[a^{5} - a^{4} - 6 a^{3} + a^{2} + 10 a + 6\) , \( -a^{3} + a^{2} + 4 a + 1\) , \( a^{5} - a^{4} - 6 a^{3} + 2 a^{2} + 10 a + 3\) , \( -30 a^{5} + 25 a^{4} + 174 a^{3} - 36 a^{2} - 279 a - 111\) , \( 381 a^{5} - 480 a^{4} - 2282 a^{3} + 1039 a^{2} + 4197 a + 1598\bigr] \) |
${y}^2+\left(a^{5}-a^{4}-6a^{3}+a^{2}+10a+6\right){x}{y}+\left(a^{5}-a^{4}-6a^{3}+2a^{2}+10a+3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a+1\right){x}^{2}+\left(-30a^{5}+25a^{4}+174a^{3}-36a^{2}-279a-111\right){x}+381a^{5}-480a^{4}-2282a^{3}+1039a^{2}+4197a+1598$ |
| 71.4-a1 |
71.4-a |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
71.4 |
\( 71 \) |
\( -71 \) |
$165.37322$ |
$(-a^4+2a^3+3a^2-5a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.043419546$ |
$16136.44718$ |
3.24033 |
\( \frac{3750585}{71} a^{5} - \frac{16668104}{71} a^{4} + \frac{10004039}{71} a^{3} + \frac{32211004}{71} a^{2} - \frac{22323259}{71} a - \frac{16869930}{71} \) |
\( \bigl[1\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 5 a - 6\) , \( a^{3} - 3 a - 2\) , \( -2 a^{4} + 5 a^{3} + 5 a^{2} - 9 a - 3\) , \( -a^{5} + a^{4} + 5 a^{3} - 8 a - 4\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}-3a-2\right){y}={x}^{3}+\left(-a^{4}+2a^{3}+5a^{2}-5a-6\right){x}^{2}+\left(-2a^{4}+5a^{3}+5a^{2}-9a-3\right){x}-a^{5}+a^{4}+5a^{3}-8a-4$ |
| 71.4-b1 |
71.4-b |
$1$ |
$1$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
71.4 |
\( 71 \) |
\( 71^{2} \) |
$165.37322$ |
$(-a^4+2a^3+3a^2-5a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$0.031027105$ |
$17568.15058$ |
5.04189 |
\( \frac{410245}{5041} a^{5} + \frac{2784718}{5041} a^{4} - \frac{6117284}{5041} a^{3} - \frac{8192443}{5041} a^{2} + \frac{8932498}{5041} a + \frac{8471844}{5041} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 6 a\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 4 a^{2} - 3 a - 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + 2 a - 2\) , \( -a^{5} + 5 a^{3} + 3 a^{2} - 6 a - 4\) , \( -a^{5} + a^{4} + 4 a^{3} - a^{2} - 4 a - 2\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+5a^{2}+6a\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+2a-2\right){y}={x}^{3}+\left(-a^{5}+2a^{4}+3a^{3}-4a^{2}-3a-1\right){x}^{2}+\left(-a^{5}+5a^{3}+3a^{2}-6a-4\right){x}-a^{5}+a^{4}+4a^{3}-a^{2}-4a-2$ |
| 71.4-c1 |
71.4-c |
$2$ |
$3$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
71.4 |
\( 71 \) |
\( - 71^{3} \) |
$165.37322$ |
$(-a^4+2a^3+3a^2-5a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$81$ |
\( 1 \) |
$1$ |
$34.24063407$ |
2.13783 |
\( \frac{18074622308423149102843876}{357911} a^{5} - \frac{74858908919538825955006516}{357911} a^{4} + \frac{13164803046658702198883171}{357911} a^{3} + \frac{219940383767839611515439765}{357911} a^{2} - \frac{124574401373439899083834841}{357911} a - \frac{110823317044260897513415352}{357911} \) |
\( \bigl[a + 1\) , \( -a^{5} + a^{4} + 6 a^{3} - 2 a^{2} - 9 a - 4\) , \( a^{5} - a^{4} - 5 a^{3} + a^{2} + 7 a + 4\) , \( 5 a^{5} - 28 a^{4} + a^{3} + 129 a^{2} - 27 a - 145\) , \( 6 a^{5} - 119 a^{4} + 119 a^{3} + 590 a^{2} - 305 a - 729\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{5}-a^{4}-5a^{3}+a^{2}+7a+4\right){y}={x}^{3}+\left(-a^{5}+a^{4}+6a^{3}-2a^{2}-9a-4\right){x}^{2}+\left(5a^{5}-28a^{4}+a^{3}+129a^{2}-27a-145\right){x}+6a^{5}-119a^{4}+119a^{3}+590a^{2}-305a-729$ |
| 71.4-c2 |
71.4-c |
$2$ |
$3$ |
6.6.1683101.1 |
$6$ |
$[6, 0]$ |
71.4 |
\( 71 \) |
\( -71 \) |
$165.37322$ |
$(-a^4+2a^3+3a^2-5a-4)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$24961.42223$ |
2.13783 |
\( \frac{82342970}{71} a^{5} - \frac{294860091}{71} a^{4} - \frac{32417041}{71} a^{3} + \frac{837693153}{71} a^{2} - \frac{357063764}{71} a - \frac{372482518}{71} \) |
\( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 5 a^{2} + 2 a - 2\) , \( 3 a^{5} - 9 a^{4} - 2 a^{3} + 16 a^{2} + a - 2\) , \( 8 a^{5} - 26 a^{4} - 3 a^{3} + 51 a^{2} - 2 a - 14\bigr] \) |
${y}^2+\left(a^{5}-2a^{4}-4a^{3}+6a^{2}+5a-2\right){x}{y}+\left(a^{5}-2a^{4}-3a^{3}+5a^{2}+2a-2\right){y}={x}^{3}+\left(a^{5}-2a^{4}-5a^{3}+7a^{2}+8a-3\right){x}^{2}+\left(3a^{5}-9a^{4}-2a^{3}+16a^{2}+a-2\right){x}+8a^{5}-26a^{4}-3a^{3}+51a^{2}-2a-14$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
