| 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 |
| 9.1-a1 |
9.1-a |
$4$ |
$6$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1863.874696$ |
1.502124713 |
\( 4189363200 a^{3} + 2075931072 a^{2} - 7387830144 a - 1678779072 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{2} - 2\) , \( a^{2} - 2\) , \( 4 a^{3} - 8 a^{2} + a + 5\) , \( -2 a^{3} + 14 a^{2} - 10 a - 5\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(4a^{3}-8a^{2}+a+5\right){x}-2a^{3}+14a^{2}-10a-5$ |
| 9.1-a2 |
9.1-a |
$4$ |
$6$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$207.0971884$ |
1.502124713 |
\( 2937600 a^{3} - 6516288 a^{2} - 7382016 a + 13364352 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 2\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 9 a^{3} - 8 a^{2} - 36 a - 6\) , \( 60 a^{3} - 47 a^{2} - 238 a - 51\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-2\right){x}^{2}+\left(9a^{3}-8a^{2}-36a-6\right){x}+60a^{3}-47a^{2}-238a-51$ |
| 9.1-a3 |
9.1-a |
$4$ |
$6$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1863.874696$ |
1.502124713 |
\( -4189363200 a^{3} + 14644020672 a^{2} - 9332121600 a - 2801314944 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{2} - a - 2\) , \( a\) , \( -3 a^{3} + a^{2} + 7 a\) , \( a^{3} - 2 a\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+a{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-3a^{3}+a^{2}+7a\right){x}+a^{3}-2a$ |
| 9.1-a4 |
9.1-a |
$4$ |
$6$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$207.0971884$ |
1.502124713 |
\( -2937600 a^{3} + 2296512 a^{2} + 11601792 a + 2403648 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 2 a\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -11 a^{3} + 26 a^{2} + 27 a - 52\) , \( -48 a^{3} + 107 a^{2} + 121 a - 220\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{3}-a^{2}-2a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a\right){x}^{2}+\left(-11a^{3}+26a^{2}+27a-52\right){x}-48a^{3}+107a^{2}+121a-220$ |
| 9.1-b1 |
9.1-b |
$6$ |
$18$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1.199731322$ |
$32.34405507$ |
1.125823332 |
\( 44330496 a^{2} - 44330496 a - 11889984 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( 0\) , \( a^{2} - a - 2\) , \( -7 a^{3} + 9 a^{2} + 15 a - 22\) , \( -25 a^{3} + 29 a^{2} + 55 a - 67\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-7a^{3}+9a^{2}+15a-22\right){x}-25a^{3}+29a^{2}+55a-67$ |
| 9.1-b2 |
9.1-b |
$6$ |
$18$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$0.133303480$ |
$2619.868460$ |
1.125823332 |
\( 44330496 a^{2} - 44330496 a - 11889984 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 2 a\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -9 a^{3} + 12 a^{2} + 19 a - 26\) , \( 17 a^{3} - 18 a^{2} - 38 a + 41\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a\right){x}^{2}+\left(-9a^{3}+12a^{2}+19a-26\right){x}+17a^{3}-18a^{2}-38a+41$ |
| 9.1-b3 |
9.1-b |
$6$ |
$18$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2 \) |
$0.399910440$ |
$873.2894869$ |
1.125823332 |
\( 1728 \) |
\( \bigl[a^{2} - a - 1\) , \( a^{2} - a - 3\) , \( 1\) , \( -a^{2} + a + 3\) , \( -1\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-a^{2}+a+3\right){x}-1$ |
| 9.1-b4 |
9.1-b |
$6$ |
$18$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3Cs.1.1 |
$1$ |
\( 2^{2} \) |
$0.199955220$ |
$873.2894869$ |
1.125823332 |
\( 1728 \) |
\( \bigl[a^{2} - a - 1\) , \( a^{2} - a - 3\) , \( a^{2} - a - 2\) , \( 0\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}$ |
| 9.1-b5 |
9.1-b |
$6$ |
$18$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 2^{2} \) |
$0.599865661$ |
$32.34405507$ |
1.125823332 |
\( -44330496 a^{2} + 44330496 a + 165432000 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( 0\) , \( 1\) , \( -11 a^{3} - a^{2} + 21 a - 4\) , \( -59 a^{3} - 22 a^{2} + 106 a + 10\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+{y}={x}^{3}+\left(-11a^{3}-a^{2}+21a-4\right){x}-59a^{3}-22a^{2}+106a+10$ |
| 9.1-b6 |
9.1-b |
$6$ |
$18$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-36$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.066651740$ |
$2619.868460$ |
1.125823332 |
\( -44330496 a^{2} + 44330496 a + 165432000 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 2 a\) , \( a^{3} - 4 a\) , \( -12 a^{3} - a^{2} + 22 a - 4\) , \( 48 a^{3} + 20 a^{2} - 86 a - 14\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a\right){x}^{2}+\left(-12a^{3}-a^{2}+22a-4\right){x}+48a^{3}+20a^{2}-86a-14$ |
| 9.1-c1 |
9.1-c |
$4$ |
$6$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$183.5898402$ |
1.331620377 |
\( 4189363200 a^{3} + 2075931072 a^{2} - 7387830144 a - 1678779072 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - 5 a - 2\) , \( a^{3} - 3 a\) , \( 3 a^{3} - 9 a^{2} + 4\) , \( 5 a^{3} - 20 a^{2} + 15 a + 2\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-5a-2\right){x}^{2}+\left(3a^{3}-9a^{2}+4\right){x}+5a^{3}-20a^{2}+15a+2$ |
| 9.1-c2 |
9.1-c |
$4$ |
$6$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1652.308562$ |
1.331620377 |
\( 2937600 a^{3} - 6516288 a^{2} - 7382016 a + 13364352 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 2\) , \( a^{2} - 1\) , \( 9 a^{3} - 8 a^{2} - 35 a - 6\) , \( -20 a^{3} + 14 a^{2} + 82 a + 17\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-2\right){x}^{2}+\left(9a^{3}-8a^{2}-35a-6\right){x}-20a^{3}+14a^{2}+82a+17$ |
| 9.1-c3 |
9.1-c |
$4$ |
$6$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$1652.308562$ |
1.331620377 |
\( -2937600 a^{3} + 2296512 a^{2} + 11601792 a + 2403648 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 2 a\) , \( a + 1\) , \( -11 a^{3} + 26 a^{2} + 28 a - 51\) , \( 33 a^{3} - 73 a^{2} - 83 a + 149\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a\right){x}^{2}+\left(-11a^{3}+26a^{2}+28a-51\right){x}+33a^{3}-73a^{2}-83a+149$ |
| 9.1-c4 |
9.1-c |
$4$ |
$6$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{3} \) |
$8.10694$ |
$(a^3-a^2-4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1$ |
$183.5898402$ |
1.331620377 |
\( -4189363200 a^{3} + 14644020672 a^{2} - 9332121600 a - 2801314944 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + 3 a + 2\) , \( a\) , \( -4 a^{3} + 11 a + 4\) , \( -4 a^{3} + 10 a + 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+3a+2\right){x}^{2}+\left(-4a^{3}+11a+4\right){x}-4a^{3}+10a+1$ |
| 16.1-a1 |
16.1-a |
$8$ |
$12$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$8.71148$ |
$(a^2-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$939.3424627$ |
1.135545375 |
\( -818626500 a^{2} + 818626500 a + 3055158000 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 18 a^{3} - 23 a^{2} - 52 a - 13\) , \( -41 a^{3} + 22 a^{2} + 184 a + 38\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+2\right){x}^{2}+\left(18a^{3}-23a^{2}-52a-13\right){x}-41a^{3}+22a^{2}+184a+38$ |
| 16.1-a2 |
16.1-a |
$8$ |
$12$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$8.71148$ |
$(a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$104.3713847$ |
1.135545375 |
\( 0 \) |
\( \bigl[0\) , \( a^{3} - 2 a^{2} - a + 2\) , \( 0\) , \( a^{2} - 2 a + 1\) , \( -49 a^{3} + 108 a^{2} + 124 a - 223\bigr] \) |
${y}^2={x}^{3}+\left(a^{3}-2a^{2}-a+2\right){x}^{2}+\left(a^{2}-2a+1\right){x}-49a^{3}+108a^{2}+124a-223$ |
| 16.1-a3 |
16.1-a |
$8$ |
$12$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$8.71148$ |
$(a^2-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$939.3424627$ |
1.135545375 |
\( 0 \) |
\( \bigl[0\) , \( -a^{3} + 2 a^{2} + a - 2\) , \( 0\) , \( a^{2} - 2 a + 1\) , \( 49 a^{3} - 108 a^{2} - 124 a + 223\bigr] \) |
${y}^2={x}^{3}+\left(-a^{3}+2a^{2}+a-2\right){x}^{2}+\left(a^{2}-2a+1\right){x}+49a^{3}-108a^{2}-124a+223$ |
| 16.1-a4 |
16.1-a |
$8$ |
$12$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$8.71148$ |
$(a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$104.3713847$ |
1.135545375 |
\( -818626500 a^{2} + 818626500 a + 3055158000 \) |
\( \bigl[a^{3} - 4 a - 1\) , \( a\) , \( 0\) , \( 17 a^{3} - 19 a^{2} - 45 a - 14\) , \( 72 a^{3} - 39 a^{2} - 316 a - 71\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}={x}^{3}+a{x}^{2}+\left(17a^{3}-19a^{2}-45a-14\right){x}+72a^{3}-39a^{2}-316a-71$ |
| 16.1-a5 |
16.1-a |
$8$ |
$12$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$8.71148$ |
$(a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2Cs, 3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$417.4855389$ |
1.135545375 |
\( 54000 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( 0\) , \( a^{2} - a - 1\) , \( -2 a^{3} + 4 a - 2\) , \( -6 a^{3} + 12 a - 4\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-2a^{3}+4a-2\right){x}-6a^{3}+12a-4$ |
| 16.1-a6 |
16.1-a |
$8$ |
$12$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$8.71148$ |
$(a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$1$ |
$104.3713847$ |
1.135545375 |
\( 818626500 a^{2} - 818626500 a - 219348000 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( 0\) , \( a^{2} - a - 1\) , \( -27 a^{3} - 10 a^{2} + 49 a + 3\) , \( -218 a^{3} - 109 a^{2} + 385 a + 88\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-27a^{3}-10a^{2}+49a+3\right){x}-218a^{3}-109a^{2}+385a+88$ |
| 16.1-a7 |
16.1-a |
$8$ |
$12$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{8} \) |
$8.71148$ |
$(a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/6\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2Cs, 3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$3757.369850$ |
1.135545375 |
\( 54000 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 2 a\) , \( a^{3} - 4 a - 1\) , \( -3 a^{3} + a^{2} + 5 a - 3\) , \( 4 a^{3} - 9 a\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a\right){x}^{2}+\left(-3a^{3}+a^{2}+5a-3\right){x}+4a^{3}-9a$ |
| 16.1-a8 |
16.1-a |
$8$ |
$12$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$8.71148$ |
$(a^2-a-1)$ |
0 |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-48$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1$ |
$939.3424627$ |
1.135545375 |
\( 818626500 a^{2} - 818626500 a - 219348000 \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 2 a\) , \( a^{3} - 4 a - 1\) , \( -28 a^{3} - 9 a^{2} + 50 a + 2\) , \( 191 a^{3} + 99 a^{2} - 337 a - 87\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{3}-4a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a\right){x}^{2}+\left(-28a^{3}-9a^{2}+50a+2\right){x}+191a^{3}+99a^{2}-337a-87$ |
| 23.1-a1 |
23.1-a |
$2$ |
$2$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$9.11576$ |
$(a^3-a^2-4a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$276.3679194$ |
2.004561649 |
\( -\frac{51871744}{529} a^{3} + \frac{181608704}{529} a^{2} - \frac{115802112}{529} a - \frac{34803520}{529} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 5 a + 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -7 a^{3} + 5 a^{2} + 26 a + 5\) , \( -9 a^{3} + 7 a^{2} + 34 a + 5\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{3}-a^{2}-3a+1\right){y}={x}^{3}+\left(-a^{3}+5a+2\right){x}^{2}+\left(-7a^{3}+5a^{2}+26a+5\right){x}-9a^{3}+7a^{2}+34a+5$ |
| 23.1-a2 |
23.1-a |
$2$ |
$2$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$9.11576$ |
$(a^3-a^2-4a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$552.7358388$ |
2.004561649 |
\( \frac{3016704}{23} a^{3} - \frac{1985280}{23} a^{2} - \frac{6025216}{23} a + \frac{5506368}{23} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{3} - 4 a - 2\) , \( a^{3} - 4 a\) , \( 4 a^{3} - 17 a^{2} + 16 a + 5\) , \( 37 a^{3} - 127 a^{2} + 76 a + 23\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-4a-2\right){x}^{2}+\left(4a^{3}-17a^{2}+16a+5\right){x}+37a^{3}-127a^{2}+76a+23$ |
| 23.1-b1 |
23.1-b |
$2$ |
$2$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( 23^{2} \) |
$9.11576$ |
$(a^3-a^2-4a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.027029851$ |
$1837.005676$ |
1.440608399 |
\( -\frac{51871744}{529} a^{3} + \frac{181608704}{529} a^{2} - \frac{115802112}{529} a - \frac{34803520}{529} \) |
\( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + a^{2} + 2 a\) , \( a^{2} - a - 2\) , \( -3 a^{3} + 2 a^{2} + 9 a + 1\) , \( -2 a^{3} + a^{2} + 7 a + 2\bigr] \) |
${y}^2+\left(a^{3}-4a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a\right){x}^{2}+\left(-3a^{3}+2a^{2}+9a+1\right){x}-2a^{3}+a^{2}+7a+2$ |
| 23.1-b2 |
23.1-b |
$2$ |
$2$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$9.11576$ |
$(a^3-a^2-4a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.054059703$ |
$1837.005676$ |
1.440608399 |
\( \frac{3016704}{23} a^{3} - \frac{1985280}{23} a^{2} - \frac{6025216}{23} a + \frac{5506368}{23} \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 4\) , \( a^{3} - 4 a\) , \( 6 a^{3} - 21 a^{2} + 8 a + 9\) , \( -28 a^{3} + 96 a^{2} - 60 a - 21\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+2a-4\right){x}^{2}+\left(6a^{3}-21a^{2}+8a+9\right){x}-28a^{3}+96a^{2}-60a-21$ |
| 23.2-a1 |
23.2-a |
$2$ |
$2$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$9.11576$ |
$(a^3-2a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$552.7358388$ |
2.004561649 |
\( -\frac{3016704}{23} a^{3} + \frac{7064832}{23} a^{2} + \frac{945664}{23} a + \frac{512576}{23} \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{3} + 4 a + 1\) , \( a^{3} - 4 a\) , \( -6 a^{3} - 3 a^{2} + 14 a + 3\) , \( -28 a^{3} - 14 a^{2} + 50 a + 11\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-6a^{3}-3a^{2}+14a+3\right){x}-28a^{3}-14a^{2}+50a+11$ |
| 23.2-a2 |
23.2-a |
$2$ |
$2$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( 23^{2} \) |
$9.11576$ |
$(a^3-2a^2-3a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$276.3679194$ |
2.004561649 |
\( \frac{51871744}{529} a^{3} + \frac{25993472}{529} a^{2} - \frac{91800064}{529} a - \frac{20868672}{529} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 4 a - 1\) , \( 1\) , \( a^{3} + 2 a\) , \( 2 a^{3} - 4 a - 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+{y}={x}^{3}+\left(a^{3}-4a-1\right){x}^{2}+\left(a^{3}+2a\right){x}+2a^{3}-4a-1$ |
| 23.2-b1 |
23.2-b |
$2$ |
$2$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$9.11576$ |
$(a^3-2a^2-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.054059703$ |
$1837.005676$ |
1.440608399 |
\( -\frac{3016704}{23} a^{3} + \frac{7064832}{23} a^{2} + \frac{945664}{23} a + \frac{512576}{23} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 4 a\) , \( -4 a^{3} - 4 a^{2} + 7 a + 4\) , \( 23 a^{3} + 10 a^{2} - 41 a - 9\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+2\right){x}^{2}+\left(-4a^{3}-4a^{2}+7a+4\right){x}+23a^{3}+10a^{2}-41a-9$ |
| 23.2-b2 |
23.2-b |
$2$ |
$2$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( 23^{2} \) |
$9.11576$ |
$(a^3-2a^2-3a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.027029851$ |
$1837.005676$ |
1.440608399 |
\( \frac{51871744}{529} a^{3} + \frac{25993472}{529} a^{2} - \frac{91800064}{529} a - \frac{20868672}{529} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{2} - a - 2\) , \( 4 a^{3} - 9 a^{2} - 8 a + 14\) , \( 2 a^{3} - 5 a^{2} - 3 a + 8\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a+4\right){x}^{2}+\left(4a^{3}-9a^{2}-8a+14\right){x}+2a^{3}-5a^{2}-3a+8$ |
| 27.1-a1 |
27.1-a |
$2$ |
$3$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$9.30031$ |
$(a^3-a^2-4a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$686.8508977$ |
1.107086983 |
\( 756 a^{3} - 1458 a^{2} - 567 a + 1674 \) |
\( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a + 1\) , \( a^{3} - 3 a - 1\) , \( -a^{3} + 3 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a-1\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(-a^{3}+3a+1\right){x}$ |
| 27.1-a2 |
27.1-a |
$2$ |
$3$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$9.30031$ |
$(a^3-a^2-4a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$76.31676641$ |
1.107086983 |
\( 538731 a^{3} + 78732 a^{2} - 1281573 a - 289404 \) |
\( \bigl[a + 1\) , \( a^{3} - 3 a - 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -a - 1\) , \( -7 a^{3} - 3 a^{2} + 12 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-a^{2}-3a+2\right){y}={x}^{3}+\left(a^{3}-3a-2\right){x}^{2}+\left(-a-1\right){x}-7a^{3}-3a^{2}+12a+1$ |
| 27.1-b1 |
27.1-b |
$2$ |
$3$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$9.30031$ |
$(a^3-a^2-4a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.036508029$ |
$302.1965489$ |
1.920529262 |
\( -756 a^{3} + 810 a^{2} + 1215 a + 405 \) |
\( \bigl[a\) , \( -a^{2} + 3\) , \( 0\) , \( a^{3} - 3 a^{2} + 4\) , \( a^{3} - 3 a^{2} + 3\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(a^{3}-3a^{2}+4\right){x}+a^{3}-3a^{2}+3$ |
| 27.1-b2 |
27.1-b |
$2$ |
$3$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$9.30031$ |
$(a^3-a^2-4a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.109524089$ |
$2719.768940$ |
1.920529262 |
\( -538731 a^{3} + 1694925 a^{2} - 492084 a - 953514 \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -1\) , \( a^{2} - a - 1\) , \( 2 a^{3} - 3 a^{2} + 4 a - 4\) , \( -a^{3} + 12 a^{2} - 14 a + 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}-{x}^{2}+\left(2a^{3}-3a^{2}+4a-4\right){x}-a^{3}+12a^{2}-14a+1$ |
| 27.1-c1 |
27.1-c |
$2$ |
$3$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$9.30031$ |
$(a^3-a^2-4a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$76.31676641$ |
1.107086983 |
\( -538731 a^{3} + 1694925 a^{2} - 492084 a - 953514 \) |
\( \bigl[a\) , \( -a^{3} + 5 a\) , \( a + 1\) , \( -a^{3} - 2 a^{2} + 11 a - 3\) , \( -3 a^{2} + 7 a - 2\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(-a^{3}-2a^{2}+11a-3\right){x}-3a^{2}+7a-2$ |
| 27.1-c2 |
27.1-c |
$2$ |
$3$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$9.30031$ |
$(a^3-a^2-4a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$686.8508977$ |
1.107086983 |
\( -756 a^{3} + 810 a^{2} + 1215 a + 405 \) |
\( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} - a^{2} + 4 a - 1\) , \( -a^{3} + a^{2} + 2 a - 2\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-2a+2\right){x}{y}+\left(a^{3}-a^{2}-2a+2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+2a-1\right){x}^{2}+\left(-a^{3}-a^{2}+4a-1\right){x}-a^{3}+a^{2}+2a-2$ |
| 27.1-d1 |
27.1-d |
$2$ |
$3$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{3} \) |
$9.30031$ |
$(a^3-a^2-4a+1)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$0.109524089$ |
$2719.768940$ |
1.920529262 |
\( 538731 a^{3} + 78732 a^{2} - 1281573 a - 289404 \) |
\( \bigl[a^{3} - 3 a\) , \( a^{3} - a^{2} - 2 a + 2\) , \( a^{3} - 3 a\) , \( 10 a^{3} + 2 a^{2} - 21 a - 3\) , \( 19 a^{3} + 10 a^{2} - 32 a - 7\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-3a\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+2\right){x}^{2}+\left(10a^{3}+2a^{2}-21a-3\right){x}+19a^{3}+10a^{2}-32a-7$ |
| 27.1-d2 |
27.1-d |
$2$ |
$3$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
27.1 |
\( 3^{3} \) |
\( - 3^{9} \) |
$9.30031$ |
$(a^3-a^2-4a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 3 \) |
$0.036508029$ |
$302.1965489$ |
1.920529262 |
\( 756 a^{3} - 1458 a^{2} - 567 a + 1674 \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( 0\) , \( -a^{3} + 3 a + 2\) , \( -a^{3} + 3 a + 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-a^{3}+3a+2\right){x}-a^{3}+3a+1$ |
| 33.1-a1 |
33.1-a |
$2$ |
$2$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{2} \cdot 11^{2} \) |
$9.53654$ |
$(a^3-a^2-4a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$176.2452005$ |
2.556695949 |
\( \frac{334152923942435}{11} a^{3} - \frac{2225144489189896}{33} a^{2} - \frac{2518541583558944}{33} a + \frac{4563125797797872}{33} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{2} - a - 1\) , \( -3 a^{3} + 10 a^{2} + 15 a - 30\) , \( -22 a^{3} + 57 a^{2} + 54 a - 110\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(-3a^{3}+10a^{2}+15a-30\right){x}-22a^{3}+57a^{2}+54a-110$ |
| 33.1-a2 |
33.1-a |
$2$ |
$2$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3 \cdot 11 \) |
$9.53654$ |
$(a^3-a^2-4a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$704.9808023$ |
2.556695949 |
\( -\frac{99319376}{33} a^{3} + \frac{64904676}{11} a^{2} + \frac{91777606}{11} a - \frac{356075639}{33} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{2} - a - 1\) , \( 2 a^{3} - 5 a\) , \( a^{3} + 2 a^{2} - a - 3\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+2\right){x}^{2}+\left(2a^{3}-5a\right){x}+a^{3}+2a^{2}-a-3$ |
| 33.1-b1 |
33.1-b |
$4$ |
$10$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{20} \cdot 11^{2} \) |
$9.53654$ |
$(a^3-a^2-4a+1), (a^2-2a-2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$329.7042412$ |
1.913138049 |
\( -\frac{2291200}{2673} a^{2} + \frac{2291200}{2673} a + \frac{6236608}{2673} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{2} - a - 2\) , \( a^{2} - a - 2\) , \( 5 a^{2} - 5 a - 17\) , \( a^{2} - a - 3\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(5a^{2}-5a-17\right){x}+a^{2}-a-3$ |
| 33.1-b2 |
33.1-b |
$4$ |
$10$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{2} \cdot 11^{20} \) |
$9.53654$ |
$(a^3-a^2-4a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.527526785$ |
1.913138049 |
\( \frac{1081911102879025664}{77812273803} a^{2} - \frac{1081911102879025664}{77812273803} a - \frac{3980255358140970688}{77812273803} \) |
\( \bigl[a^{2} - a - 1\) , \( 0\) , \( 1\) , \( -76 a^{2} + 76 a - 127\) , \( -795 a^{2} + 795 a - 485\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+{y}={x}^{3}+\left(-76a^{2}+76a-127\right){x}-795a^{2}+795a-485$ |
| 33.1-b3 |
33.1-b |
$4$ |
$10$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{10} \cdot 11^{4} \) |
$9.53654$ |
$(a^3-a^2-4a+1), (a^2-2a-2)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$329.7042412$ |
1.913138049 |
\( \frac{2084278784}{3267} a^{2} - \frac{2084278784}{3267} a - \frac{553870528}{3267} \) |
\( \bigl[a^{2} - a - 1\) , \( 0\) , \( 1\) , \( -6 a^{2} + 6 a + 3\) , \( 6 a^{2} - 6 a - 2\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+{y}={x}^{3}+\left(-6a^{2}+6a+3\right){x}+6a^{2}-6a-2$ |
| 33.1-b4 |
33.1-b |
$4$ |
$10$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{4} \cdot 11^{10} \) |
$9.53654$ |
$(a^3-a^2-4a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$25$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.527526785$ |
1.913138049 |
\( -\frac{313724549420617141760}{483153} a^{2} + \frac{313724549420617141760}{483153} a + \frac{390278652673081146176}{161051} \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 2\) , \( a^{2} - a - 2\) , \( -287 a^{2} + 287 a + 35\) , \( -9361 a^{2} + 9361 a + 2375\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-287a^{2}+287a+35\right){x}-9361a^{2}+9361a+2375$ |
| 33.1-c1 |
33.1-c |
$2$ |
$2$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{2} \cdot 11^{2} \) |
$9.53654$ |
$(a^3-a^2-4a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$116.7168136$ |
1.693149111 |
\( \frac{334152923942435}{11} a^{3} - \frac{2225144489189896}{33} a^{2} - \frac{2518541583558944}{33} a + \frac{4563125797797872}{33} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 3 a\) , \( a^{3} - 4 a\) , \( -5 a^{3} + 11 a^{2} + 20 a - 33\) , \( 18 a^{3} - 47 a^{2} - 36 a + 78\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(-5a^{3}+11a^{2}+20a-33\right){x}+18a^{3}-47a^{2}-36a+78$ |
| 33.1-c2 |
33.1-c |
$2$ |
$2$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3 \cdot 11 \) |
$9.53654$ |
$(a^3-a^2-4a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$466.8672547$ |
1.693149111 |
\( -\frac{99319376}{33} a^{3} + \frac{64904676}{11} a^{2} + \frac{91777606}{11} a - \frac{356075639}{33} \) |
\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 3 a\) , \( a^{3} - 4 a\) , \( a^{2} - 3\) , \( -2 a^{2} - a + 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-3a+1\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(a^{2}-3\right){x}-2a^{2}-a+1$ |
| 33.1-d1 |
33.1-d |
$4$ |
$10$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{20} \cdot 11^{2} \) |
$9.53654$ |
$(a^3-a^2-4a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$77.21805217$ |
1.120161460 |
\( -\frac{2291200}{2673} a^{2} + \frac{2291200}{2673} a + \frac{6236608}{2673} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{2} - a - 1\) , \( 1\) , \( 6 a^{2} - 6 a - 17\) , \( -3 a^{2} + 3 a + 14\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+{y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(6a^{2}-6a-17\right){x}-3a^{2}+3a+14$ |
| 33.1-d2 |
33.1-d |
$4$ |
$10$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{4} \cdot 11^{10} \) |
$9.53654$ |
$(a^3-a^2-4a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$77.21805217$ |
1.120161460 |
\( -\frac{313724549420617141760}{483153} a^{2} + \frac{313724549420617141760}{483153} a + \frac{390278652673081146176}{161051} \) |
\( \bigl[a^{2} - a - 1\) , \( 1\) , \( a^{2} - a - 2\) , \( -286 a^{2} + 286 a + 34\) , \( 9075 a^{2} - 9075 a - 2342\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+{x}^{2}+\left(-286a^{2}+286a+34\right){x}+9075a^{2}-9075a-2342$ |
| 33.1-d3 |
33.1-d |
$4$ |
$10$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{2} \cdot 11^{20} \) |
$9.53654$ |
$(a^3-a^2-4a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2^{2} \) |
$1$ |
$77.21805217$ |
1.120161460 |
\( \frac{1081911102879025664}{77812273803} a^{2} - \frac{1081911102879025664}{77812273803} a - \frac{3980255358140970688}{77812273803} \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 3\) , \( 1\) , \( -77 a^{2} + 77 a - 124\) , \( 719 a^{2} - 719 a + 358\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-77a^{2}+77a-124\right){x}+719a^{2}-719a+358$ |
| 33.1-d4 |
33.1-d |
$4$ |
$10$ |
4.4.4752.1 |
$4$ |
$[4, 0]$ |
33.1 |
\( 3 \cdot 11 \) |
\( 3^{10} \cdot 11^{4} \) |
$9.53654$ |
$(a^3-a^2-4a+1), (a^2-2a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
✓ |
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$77.21805217$ |
1.120161460 |
\( \frac{2084278784}{3267} a^{2} - \frac{2084278784}{3267} a - \frac{553870528}{3267} \) |
\( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 3\) , \( 1\) , \( -7 a^{2} + 7 a + 6\) , \( -12 a^{2} + 12 a + 5\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-7a^{2}+7a+6\right){x}-12a^{2}+12a+5$ |
*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.
