| 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 |
| 16.1-a1 |
16.1-a |
$2$ |
$3$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{12} \) |
$16.82467$ |
$(2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1.936875010$ |
$208.4822349$ |
4.044047655 |
\( -\frac{35465}{8} a^{3} - \frac{32537}{8} a^{2} + \frac{258129}{8} a + \frac{364499}{8} \) |
\( \bigl[a^{3} - a^{2} - 6 a + 1\) , \( a^{2} - 2 a - 6\) , \( a^{2} - a - 6\) , \( 2 a^{3} - 2 a^{2} - 10 a + 1\) , \( 10 a^{3} - 32 a^{2} - 37 a + 132\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a+1\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(2a^{3}-2a^{2}-10a+1\right){x}+10a^{3}-32a^{2}-37a+132$ |
| 16.1-a2 |
16.1-a |
$2$ |
$3$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{4} \) |
$16.82467$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$5.810625031$ |
$2.573854752$ |
4.044047655 |
\( -\frac{23743655335517}{2} a^{3} - 15479984690090 a^{2} + \frac{182490717514631}{2} a + 147206099994603 \) |
\( \bigl[a^{3} - a^{2} - 6 a + 1\) , \( a^{2} - 2 a - 6\) , \( a^{2} - a - 6\) , \( 152 a^{3} - 632 a^{2} - 350 a + 2591\) , \( 2636 a^{3} - 11350 a^{2} - 5341 a + 46488\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a+1\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a^{2}-2a-6\right){x}^{2}+\left(152a^{3}-632a^{2}-350a+2591\right){x}+2636a^{3}-11350a^{2}-5341a+46488$ |
| 16.1-b1 |
16.1-b |
$2$ |
$3$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$16.82467$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.024742063$ |
$1603.715366$ |
3.576443180 |
\( -\frac{96291}{8} a^{3} + \frac{412803}{8} a^{2} + \frac{56189}{2} a - 220208 \) |
\( \bigl[a^{3} - 7 a - 7\) , \( a^{3} - 7 a - 7\) , \( 0\) , \( 8 a^{3} - 2 a^{2} - 47 a - 38\) , \( 3 a^{3} + 42 a^{2} - 64 a - 234\bigr] \) |
${y}^2+\left(a^{3}-7a-7\right){x}{y}={x}^{3}+\left(a^{3}-7a-7\right){x}^{2}+\left(8a^{3}-2a^{2}-47a-38\right){x}+3a^{3}+42a^{2}-64a-234$ |
| 16.1-b2 |
16.1-b |
$2$ |
$3$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.82467$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.074226190$ |
$1603.715366$ |
3.576443180 |
\( \frac{13157909}{2} a^{3} + 8591409 a^{2} - \frac{101195049}{2} a - \frac{163362181}{2} \) |
\( \bigl[1\) , \( -a^{2} + a + 8\) , \( a + 1\) , \( -3 a^{2} + a + 19\) , \( a^{3} - a^{2} - 7 a + 1\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+a+8\right){x}^{2}+\left(-3a^{2}+a+19\right){x}+a^{3}-a^{2}-7a+1$ |
| 16.1-c1 |
16.1-c |
$2$ |
$3$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{4} \) |
$16.82467$ |
$(2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
|
\( 1 \) |
$1$ |
$2.573854752$ |
4.044047655 |
\( \frac{23743655335517}{2} a^{3} - \frac{102190935386731}{2} a^{2} - 24669906373860 a + 211099646394070 \) |
\( \bigl[a^{3} - 7 a - 7\) , \( -a^{3} + 7 a + 8\) , \( a\) , \( -155 a^{3} - 181 a^{2} + 1187 a + 1810\) , \( -2555 a^{3} - 3316 a^{2} + 19512 a + 31312\bigr] \) |
${y}^2+\left(a^{3}-7a-7\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+7a+8\right){x}^{2}+\left(-155a^{3}-181a^{2}+1187a+1810\right){x}-2555a^{3}-3316a^{2}+19512a+31312$ |
| 16.1-c2 |
16.1-c |
$2$ |
$3$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{12} \) |
$16.82467$ |
$(2)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 3 \) |
$1$ |
$208.4822349$ |
4.044047655 |
\( \frac{35465}{8} a^{3} - \frac{34733}{2} a^{2} - \frac{21665}{2} a + \frac{277313}{4} \) |
\( \bigl[a^{3} - a^{2} - 7 a + 1\) , \( -a^{3} + 2 a^{2} + 5 a - 7\) , \( a^{3} - a^{2} - 6 a + 1\) , \( -15 a^{3} - 15 a^{2} + 112 a + 160\) , \( -40 a^{3} - 51 a^{2} + 307 a + 490\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-7a+1\right){x}{y}+\left(a^{3}-a^{2}-6a+1\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+5a-7\right){x}^{2}+\left(-15a^{3}-15a^{2}+112a+160\right){x}-40a^{3}-51a^{2}+307a+490$ |
| 16.1-d1 |
16.1-d |
$2$ |
$3$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{12} \) |
$16.82467$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$0.024742063$ |
$1603.715366$ |
3.576443180 |
\( \frac{96291}{8} a^{3} + \frac{61965}{4} a^{2} - \frac{761489}{8} a - \frac{305099}{2} \) |
\( \bigl[a^{3} - a^{2} - 6 a + 1\) , \( a^{3} - 2 a^{2} - 6 a + 6\) , \( a^{3} - 7 a - 7\) , \( -6 a^{2} + 3 a + 35\) , \( -2 a^{3} - 5 a^{2} + 21 a + 48\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a+1\right){x}{y}+\left(a^{3}-7a-7\right){y}={x}^{3}+\left(a^{3}-2a^{2}-6a+6\right){x}^{2}+\left(-6a^{2}+3a+35\right){x}-2a^{3}-5a^{2}+21a+48$ |
| 16.1-d2 |
16.1-d |
$2$ |
$3$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$16.82467$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$0.074226190$ |
$1603.715366$ |
3.576443180 |
\( -\frac{13157909}{2} a^{3} + \frac{56656545}{2} a^{2} + 13677843 a - \frac{234216503}{2} \) |
\( \bigl[1\) , \( -a^{2} + a + 8\) , \( a\) , \( -3 a^{2} + 4 a + 18\) , \( -a^{3} + 2 a^{2} + 5 a - 5\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+8\right){x}^{2}+\left(-3a^{2}+4a+18\right){x}-a^{3}+2a^{2}+5a-5$ |
| 19.1-a1 |
19.1-a |
$2$ |
$3$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( -19 \) |
$17.19000$ |
$(-a-1)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 1 \) |
$1$ |
$460.0279088$ |
3.134026093 |
\( \frac{14048}{19} a^{3} - \frac{58655}{19} a^{2} - \frac{53605}{19} a + \frac{337746}{19} \) |
\( \bigl[a^{2} - 7\) , \( 0\) , \( a^{3} - 8 a - 7\) , \( 2 a^{3} - 13 a - 6\) , \( 5 a^{3} + 6 a^{2} - 40 a - 63\bigr] \) |
${y}^2+\left(a^{2}-7\right){x}{y}+\left(a^{3}-8a-7\right){y}={x}^{3}+\left(2a^{3}-13a-6\right){x}+5a^{3}+6a^{2}-40a-63$ |
| 19.1-a2 |
19.1-a |
$2$ |
$3$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( - 19^{3} \) |
$17.19000$ |
$(-a-1)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
|
\( 3 \) |
$1$ |
$5.679356899$ |
3.134026093 |
\( \frac{188673649573644}{6859} a^{3} - \frac{732188544028507}{6859} a^{2} - \frac{886442686066785}{6859} a + \frac{4116174585951409}{6859} \) |
\( \bigl[a^{2} - 7\) , \( 0\) , \( a^{3} - 8 a - 7\) , \( -23 a^{3} - 20 a^{2} + 172 a + 219\) , \( -190 a^{3} - 208 a^{2} + 1436 a + 2087\bigr] \) |
${y}^2+\left(a^{2}-7\right){x}{y}+\left(a^{3}-8a-7\right){y}={x}^{3}+\left(-23a^{3}-20a^{2}+172a+219\right){x}-190a^{3}-208a^{2}+1436a+2087$ |
| 19.1-b1 |
19.1-b |
$1$ |
$1$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
19.1 |
\( 19 \) |
\( 19^{3} \) |
$17.19000$ |
$(-a-1)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
|
\( 3 \) |
$1$ |
$186.1593507$ |
3.430728841 |
\( -\frac{2454829497}{6859} a^{3} - \frac{3223188207}{6859} a^{2} + \frac{18885670830}{6859} a + \frac{30593217186}{6859} \) |
\( \bigl[a^{3} - a^{2} - 6 a\) , \( -a^{3} + 2 a^{2} + 7 a - 7\) , \( a^{3} - a^{2} - 6 a\) , \( a^{3} - 5 a^{2} - a + 33\) , \( 2 a^{2} + a - 11\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a\right){x}{y}+\left(a^{3}-a^{2}-6a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+7a-7\right){x}^{2}+\left(a^{3}-5a^{2}-a+33\right){x}+2a^{2}+a-11$ |
| 19.2-a1 |
19.2-a |
$1$ |
$1$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
19.2 |
\( 19 \) |
\( 19^{3} \) |
$17.19000$ |
$(-a^3+7a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$153.3581516$ |
1.151897256 |
\( \frac{90275715}{6859} a^{3} - \frac{382556601}{6859} a^{2} - \frac{196372188}{6859} a + \frac{1560776148}{6859} \) |
\( \bigl[a + 1\) , \( -a^{2} + a + 8\) , \( a^{2} - 7\) , \( 9 a^{3} - 44 a^{2} - 11 a + 192\) , \( -42 a^{3} + 177 a^{2} + 94 a - 727\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-7\right){y}={x}^{3}+\left(-a^{2}+a+8\right){x}^{2}+\left(9a^{3}-44a^{2}-11a+192\right){x}-42a^{3}+177a^{2}+94a-727$ |
| 19.3-a1 |
19.3-a |
$1$ |
$1$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
19.3 |
\( 19 \) |
\( 19^{3} \) |
$17.19000$ |
$(-a^2+2a+5)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$153.3581516$ |
1.151897256 |
\( -\frac{90275715}{6859} a^{3} - \frac{111729456}{6859} a^{2} + \frac{690658245}{6859} a + \frac{1072123074}{6859} \) |
\( \bigl[a\) , \( -a^{2} + 6\) , \( a^{2} - a - 6\) , \( -10 a^{3} - 13 a^{2} + 76 a + 125\) , \( 51 a^{3} + 66 a^{2} - 392 a - 630\bigr] \) |
${y}^2+a{x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(-a^{2}+6\right){x}^{2}+\left(-10a^{3}-13a^{2}+76a+125\right){x}+51a^{3}+66a^{2}-392a-630$ |
| 19.4-a1 |
19.4-a |
$2$ |
$3$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
19.4 |
\( 19 \) |
\( -19 \) |
$17.19000$ |
$(a^3-3a^2-5a+14)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 1 \) |
$1$ |
$460.0279088$ |
3.134026093 |
\( -\frac{14048}{19} a^{3} - 869 a^{2} + \frac{128771}{19} a + \frac{239534}{19} \) |
\( \bigl[a^{2} - 6\) , \( -a^{3} + a^{2} + 6 a\) , \( a^{3} - a^{2} - 7 a\) , \( -3 a^{3} + 7 a^{2} + 13 a - 16\) , \( -4 a^{3} + 19 a^{2} + 6 a - 84\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{3}-a^{2}-7a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a\right){x}^{2}+\left(-3a^{3}+7a^{2}+13a-16\right){x}-4a^{3}+19a^{2}+6a-84$ |
| 19.4-a2 |
19.4-a |
$2$ |
$3$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
19.4 |
\( 19 \) |
\( - 19^{3} \) |
$17.19000$ |
$(a^3-3a^2-5a+14)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
|
\( 3 \) |
$1$ |
$5.679356899$ |
3.134026093 |
\( -\frac{188673649573644}{6859} a^{3} - \frac{8745662910925}{361} a^{2} + \frac{1784798825402867}{6859} a + \frac{2686217005429761}{6859} \) |
\( \bigl[a^{2} - 6\) , \( -a^{3} + a^{2} + 6 a\) , \( a^{3} - a^{2} - 7 a\) , \( 22 a^{3} - 88 a^{2} - 57 a + 349\) , \( 191 a^{3} - 780 a^{2} - 457 a + 3133\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{3}-a^{2}-7a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a\right){x}^{2}+\left(22a^{3}-88a^{2}-57a+349\right){x}+191a^{3}-780a^{2}-457a+3133$ |
| 19.4-b1 |
19.4-b |
$1$ |
$1$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
19.4 |
\( 19 \) |
\( 19^{3} \) |
$17.19000$ |
$(a^3-3a^2-5a+14)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3 \) |
$0.204462380$ |
$186.1593507$ |
3.430728841 |
\( \frac{2454829497}{6859} a^{3} - \frac{557246142}{361} a^{2} - \frac{5074805925}{6859} a + \frac{43800870312}{6859} \) |
\( \bigl[a^{3} - 7 a - 6\) , \( 1\) , \( a^{3} - a^{2} - 6 a + 1\) , \( 3 a^{3} + 3 a^{2} - 22 a - 33\) , \( 6 a^{3} + 7 a^{2} - 45 a - 71\bigr] \) |
${y}^2+\left(a^{3}-7a-6\right){x}{y}+\left(a^{3}-a^{2}-6a+1\right){y}={x}^{3}+{x}^{2}+\left(3a^{3}+3a^{2}-22a-33\right){x}+6a^{3}+7a^{2}-45a-71$ |
| 41.1-a1 |
41.1-a |
$4$ |
$6$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41^{3} \) |
$18.92473$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 1 \) |
$1$ |
$119.1725003$ |
2.014027738 |
\( -\frac{67836429064}{68921} a^{3} - \frac{59155787416}{68921} a^{2} + \frac{643726665748}{68921} a + \frac{967482551341}{68921} \) |
\( \bigl[a^{3} - 7 a - 7\) , \( a^{3} - 8 a - 7\) , \( a^{3} - a^{2} - 7 a + 1\) , \( 3 a^{3} + 3 a^{2} - 23 a - 33\) , \( 3 a^{3} + 6 a^{2} - 25 a - 53\bigr] \) |
${y}^2+\left(a^{3}-7a-7\right){x}{y}+\left(a^{3}-a^{2}-7a+1\right){y}={x}^{3}+\left(a^{3}-8a-7\right){x}^{2}+\left(3a^{3}+3a^{2}-23a-33\right){x}+3a^{3}+6a^{2}-25a-53$ |
| 41.1-a2 |
41.1-a |
$4$ |
$6$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{6} \) |
$18.92473$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$59.58625018$ |
2.014027738 |
\( \frac{1496441838018450}{4750104241} a^{3} + \frac{3189678014230190}{4750104241} a^{2} - \frac{13956427652448924}{4750104241} a - \frac{21737388784486451}{4750104241} \) |
\( \bigl[a^{2} - 6\) , \( a^{3} - 9 a - 8\) , \( a^{3} - a^{2} - 7 a + 1\) , \( -12 a^{3} + 31 a^{2} + 71 a - 150\) , \( -52 a^{3} + 201 a^{2} + 243 a - 1144\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+\left(a^{3}-a^{2}-7a+1\right){y}={x}^{3}+\left(a^{3}-9a-8\right){x}^{2}+\left(-12a^{3}+31a^{2}+71a-150\right){x}-52a^{3}+201a^{2}+243a-1144$ |
| 41.1-a3 |
41.1-a |
$4$ |
$6$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( - 41^{2} \) |
$18.92473$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$59.58625018$ |
2.014027738 |
\( \frac{282167722336224722357}{1681} a^{3} - \frac{1092885350256385553234}{1681} a^{2} - \frac{1338845671365342370879}{1681} a + \frac{6176074444774482460203}{1681} \) |
\( \bigl[a^{3} - a^{2} - 7 a\) , \( -a^{3} + a^{2} + 7 a\) , \( a^{2} - 6\) , \( 9 a^{3} - 84 a^{2} + 44 a + 440\) , \( 62 a^{3} - 404 a^{2} + 67 a + 1949\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-7a\right){x}{y}+\left(a^{2}-6\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a\right){x}^{2}+\left(9a^{3}-84a^{2}+44a+440\right){x}+62a^{3}-404a^{2}+67a+1949$ |
| 41.1-a4 |
41.1-a |
$4$ |
$6$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
41.1 |
\( 41 \) |
\( 41 \) |
$18.92473$ |
$(a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 1 \) |
$1$ |
$119.1725003$ |
2.014027738 |
\( -\frac{5198737071}{41} a^{3} + \frac{20153956486}{41} a^{2} + \frac{24553872202}{41} a - \frac{113615145957}{41} \) |
\( \bigl[a^{3} - a^{2} - 6 a\) , \( a - 1\) , \( 0\) , \( 14 a^{3} - 110 a - 112\) , \( -3 a^{3} - 28 a^{2} + 71 a + 211\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(14a^{3}-110a-112\right){x}-3a^{3}-28a^{2}+71a+211$ |
| 41.2-a1 |
41.2-a |
$4$ |
$6$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
41.2 |
\( 41 \) |
\( 41 \) |
$18.92473$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 1 \) |
$1$ |
$119.1725003$ |
2.014027738 |
\( \frac{5198737071}{41} a^{3} + \frac{4557745273}{41} a^{2} - \frac{49265573961}{41} a - 1807464740 \) |
\( \bigl[a^{3} - 7 a - 6\) , \( -a^{3} + a^{2} + 7 a\) , \( a^{2} - a - 7\) , \( -10 a^{3} + 35 a^{2} + 51 a - 188\) , \( 17 a^{3} - 121 a^{2} - 48 a + 741\bigr] \) |
${y}^2+\left(a^{3}-7a-6\right){x}{y}+\left(a^{2}-a-7\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a\right){x}^{2}+\left(-10a^{3}+35a^{2}+51a-188\right){x}+17a^{3}-121a^{2}-48a+741$ |
| 41.2-a2 |
41.2-a |
$4$ |
$6$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
41.2 |
\( 41 \) |
\( - 41^{2} \) |
$18.92473$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$59.58625018$ |
2.014027738 |
\( -\frac{282167722336224722357}{1681} a^{3} - \frac{246382183247711386163}{1681} a^{2} + \frac{2678113204869439310276}{1681} a + \frac{98207588914365347767}{41} \) |
\( \bigl[a^{3} - 7 a - 6\) , \( -a^{3} + a^{2} + 7 a\) , \( a^{2} - a - 7\) , \( 30 a^{3} - 120 a^{2} - 139 a + 687\) , \( 97 a^{3} - 428 a^{2} - 430 a + 2471\bigr] \) |
${y}^2+\left(a^{3}-7a-6\right){x}{y}+\left(a^{2}-a-7\right){y}={x}^{3}+\left(-a^{3}+a^{2}+7a\right){x}^{2}+\left(30a^{3}-120a^{2}-139a+687\right){x}+97a^{3}-428a^{2}-430a+2471$ |
| 41.2-a3 |
41.2-a |
$4$ |
$6$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
41.2 |
\( 41 \) |
\( 41^{3} \) |
$18.92473$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 1 \) |
$1$ |
$119.1725003$ |
2.014027738 |
\( \frac{67836429064}{68921} a^{3} - \frac{262665074608}{68921} a^{2} - \frac{321905803724}{68921} a + \frac{36200414649}{1681} \) |
\( \bigl[a^{3} - a^{2} - 6 a + 1\) , \( a^{3} - 2 a^{2} - 5 a + 8\) , \( a^{3} - a^{2} - 7 a\) , \( 7 a^{3} + 5 a^{2} - 51 a - 63\) , \( 12 a^{3} + 14 a^{2} - 92 a - 142\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a+1\right){x}{y}+\left(a^{3}-a^{2}-7a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-5a+8\right){x}^{2}+\left(7a^{3}+5a^{2}-51a-63\right){x}+12a^{3}+14a^{2}-92a-142$ |
| 41.2-a4 |
41.2-a |
$4$ |
$6$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
41.2 |
\( 41 \) |
\( - 41^{6} \) |
$18.92473$ |
$(a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$9$ |
\( 2 \) |
$1$ |
$59.58625018$ |
2.014027738 |
\( -\frac{1496441838018450}{4750104241} a^{3} + \frac{7679003528285540}{4750104241} a^{2} + \frac{3087746109933194}{4750104241} a - \frac{756285282553335}{115856201} \) |
\( \bigl[a^{3} - a^{2} - 6 a + 1\) , \( a^{3} - 2 a^{2} - 5 a + 8\) , \( a^{3} - a^{2} - 7 a\) , \( 12 a^{3} - 15 a^{2} - 66 a + 12\) , \( 23 a^{3} - 41 a^{2} - 113 a + 84\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-6a+1\right){x}{y}+\left(a^{3}-a^{2}-7a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-5a+8\right){x}^{2}+\left(12a^{3}-15a^{2}-66a+12\right){x}+23a^{3}-41a^{2}-113a+84$ |
| 49.1-a1 |
49.1-a |
$4$ |
$4$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{24} \) |
$19.35112$ |
$(a^2-10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.077955295$ |
$19.60597293$ |
1.904922331 |
\( \frac{221757824275299}{13841287201} a^{3} + \frac{544265756337879}{13841287201} a^{2} - \frac{93164073307983}{1977326743} a - \frac{1664008534229859}{13841287201} \) |
\( \bigl[a^{3} - 8 a - 7\) , \( -1\) , \( a^{2} - a - 6\) , \( -316 a^{3} + 1392 a^{2} + 609 a - 5812\) , \( -5945 a^{3} + 25549 a^{2} + 12413 a - 105480\bigr] \) |
${y}^2+\left(a^{3}-8a-7\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}-{x}^{2}+\left(-316a^{3}+1392a^{2}+609a-5812\right){x}-5945a^{3}+25549a^{2}+12413a-105480$ |
| 49.1-a2 |
49.1-a |
$4$ |
$4$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$19.35112$ |
$(a^2-10)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1.077955295$ |
$78.42389172$ |
1.904922331 |
\( -\frac{1305047204432928684048645}{343} a^{3} - 3322263442805961523191 a^{2} + \frac{12386477525608456648260111}{343} a + \frac{18622920688911913805531829}{343} \) |
\( \bigl[a^{2} - 7\) , \( a^{3} - a^{2} - 8 a + 1\) , \( a^{3} - 8 a - 6\) , \( -271 a^{3} + 578 a^{2} + 1550 a - 2816\) , \( -2564 a^{3} + 15531 a^{2} + 9010 a - 93150\bigr] \) |
${y}^2+\left(a^{2}-7\right){x}{y}+\left(a^{3}-8a-6\right){y}={x}^{3}+\left(a^{3}-a^{2}-8a+1\right){x}^{2}+\left(-271a^{3}+578a^{2}+1550a-2816\right){x}-2564a^{3}+15531a^{2}+9010a-93150$ |
| 49.1-a3 |
49.1-a |
$4$ |
$4$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{12} \) |
$19.35112$ |
$(a^2-10)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.538977647$ |
$313.6955668$ |
1.904922331 |
\( -\frac{2227572152555895}{117649} a^{3} - \frac{1945063396166130}{117649} a^{2} + \frac{21142355902651143}{117649} a + \frac{31787279706654594}{117649} \) |
\( \bigl[a^{2} - 7\) , \( a^{3} - a^{2} - 8 a + 1\) , \( a^{3} - 8 a - 6\) , \( -21 a^{3} + 23 a^{2} + 135 a - 66\) , \( -97 a^{3} + 260 a^{2} + 524 a - 1361\bigr] \) |
${y}^2+\left(a^{2}-7\right){x}{y}+\left(a^{3}-8a-6\right){y}={x}^{3}+\left(a^{3}-a^{2}-8a+1\right){x}^{2}+\left(-21a^{3}+23a^{2}+135a-66\right){x}-97a^{3}+260a^{2}+524a-1361$ |
| 49.1-a4 |
49.1-a |
$4$ |
$4$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$19.35112$ |
$(a^2-10)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.269488823$ |
$1254.782267$ |
1.904922331 |
\( -\frac{72741807}{343} a^{3} + 1132866 a^{2} + \frac{41876676}{343} a - \frac{1756222938}{343} \) |
\( \bigl[a^{2} - 7\) , \( a^{3} - a^{2} - 8 a + 1\) , \( a^{3} - 8 a - 6\) , \( -a^{3} + 8 a^{2} + 5 a - 41\) , \( 3 a^{3} + 2 a^{2} - 25 a - 31\bigr] \) |
${y}^2+\left(a^{2}-7\right){x}{y}+\left(a^{3}-8a-6\right){y}={x}^{3}+\left(a^{3}-a^{2}-8a+1\right){x}^{2}+\left(-a^{3}+8a^{2}+5a-41\right){x}+3a^{3}+2a^{2}-25a-31$ |
| 49.2-a1 |
49.2-a |
$4$ |
$4$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$19.35112$ |
$(a^3+a^2-8a-13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1.077955295$ |
$78.42389172$ |
1.904922331 |
\( \frac{1305047204432928684048645}{343} a^{3} - \frac{5054677974181230854600448}{343} a^{2} - \frac{6192263190544780991205150}{343} a + \frac{28564814649204996967288782}{343} \) |
\( \bigl[a^{3} - 7 a - 7\) , \( -a^{3} + 7 a + 6\) , \( 0\) , \( 658 a^{3} - 2703 a^{2} - 1553 a + 10895\) , \( -20424 a^{3} + 89053 a^{2} + 40801 a - 370274\bigr] \) |
${y}^2+\left(a^{3}-7a-7\right){x}{y}={x}^{3}+\left(-a^{3}+7a+6\right){x}^{2}+\left(658a^{3}-2703a^{2}-1553a+10895\right){x}-20424a^{3}+89053a^{2}+40801a-370274$ |
| 49.2-a2 |
49.2-a |
$4$ |
$4$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{6} \) |
$19.35112$ |
$(a^3+a^2-8a-13)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.269488823$ |
$1254.782267$ |
1.904922331 |
\( \frac{72741807}{343} a^{3} + \frac{170347617}{343} a^{2} - \frac{600797331}{343} a - \frac{1398515031}{343} \) |
\( \bigl[a^{2} - 6\) , \( a^{3} - 8 a - 7\) , \( a\) , \( 3 a^{3} + 15 a^{2} - 43 a - 113\) , \( -14 a^{3} - 22 a^{2} + 151 a + 268\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-8a-7\right){x}^{2}+\left(3a^{3}+15a^{2}-43a-113\right){x}-14a^{3}-22a^{2}+151a+268$ |
| 49.2-a3 |
49.2-a |
$4$ |
$4$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{12} \) |
$19.35112$ |
$(a^3+a^2-8a-13)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.538977647$ |
$313.6955668$ |
1.904922331 |
\( \frac{2227572152555895}{117649} a^{3} - \frac{8627779853833815}{117649} a^{2} - \frac{10569512652651198}{117649} a + \frac{48757000060583712}{117649} \) |
\( \bigl[a^{2} - 6\) , \( a^{3} - 8 a - 7\) , \( a\) , \( 23 a^{3} - 30 a^{2} - 143 a - 13\) , \( 31 a^{3} - 19 a^{2} - 224 a - 150\bigr] \) |
${y}^2+\left(a^{2}-6\right){x}{y}+a{y}={x}^{3}+\left(a^{3}-8a-7\right){x}^{2}+\left(23a^{3}-30a^{2}-143a-13\right){x}+31a^{3}-19a^{2}-224a-150$ |
| 49.2-a4 |
49.2-a |
$4$ |
$4$ |
4.4.17725.1 |
$4$ |
$[4, 0]$ |
49.2 |
\( 7^{2} \) |
\( 7^{24} \) |
$19.35112$ |
$(a^3+a^2-8a-13)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.077955295$ |
$19.60597293$ |
1.904922331 |
\( -\frac{221757824275299}{13841287201} a^{3} + \frac{172791318451968}{1977326743} a^{2} - \frac{1101656472345774}{13841287201} a - \frac{221447638110366}{1977326743} \) |
\( \bigl[a^{3} - a^{2} - 7 a\) , \( a^{3} - 2 a^{2} - 7 a + 7\) , \( a^{2} - a - 6\) , \( 316 a^{3} + 444 a^{2} - 2446 a - 4126\) , \( 5945 a^{3} + 7714 a^{2} - 45676 a - 73463\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-7a\right){x}{y}+\left(a^{2}-a-6\right){y}={x}^{3}+\left(a^{3}-2a^{2}-7a+7\right){x}^{2}+\left(316a^{3}+444a^{2}-2446a-4126\right){x}+5945a^{3}+7714a^{2}-45676a-73463$ |
*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.
