| 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 |
| 1.1-a1 |
1.1-a |
$4$ |
$15$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.79457$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$3, 5$ |
3B.1.2, 5B.4.1 |
$9$ |
\( 1 \) |
$1$ |
$4.181921816$ |
0.580410711 |
\( -1407628760845 a^{3} + 1407628760845 a^{2} + 8445772565070 a - 3086342051803 \) |
\( \bigl[-a^{3} + 2 a^{2} + 3 a - 1\) , \( 0\) , \( a^{2} - a - 2\) , \( -5 a^{2} + a\) , \( -18 a^{3} - 47 a^{2} - 9 a + 7\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+3a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(-5a^{2}+a\right){x}-18a^{3}-47a^{2}-9a+7$ |
| 1.1-a2 |
1.1-a |
$4$ |
$15$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.79457$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$3, 5$ |
3B.1.1, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$338.7356671$ |
0.580410711 |
\( -3515 a^{3} + 3515 a^{2} + 21090 a - 7688 \) |
\( \bigl[-a^{3} + 2 a^{2} + 3 a - 1\) , \( 0\) , \( a^{2} - a - 2\) , \( a\) , \( a^{3} + a^{2} - a - 1\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+3a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+a{x}+a^{3}+a^{2}-a-1$ |
| 1.1-a3 |
1.1-a |
$4$ |
$15$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.79457$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$3, 5$ |
3B.1.2, 5B.4.2 |
$9$ |
\( 1 \) |
$1$ |
$4.181921816$ |
0.580410711 |
\( 1407628760845 a^{3} - 1407628760845 a^{2} - 8445772565070 a - 4493970812648 \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( a^{2} - 2 a - 1\) , \( 5 a^{3} - a^{2} - 28 a - 28\) , \( -8 a^{3} + 43 a^{2} - 4 a - 153\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+1\right){x}^{2}+\left(5a^{3}-a^{2}-28a-28\right){x}-8a^{3}+43a^{2}-4a-153$ |
| 1.1-a4 |
1.1-a |
$4$ |
$15$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$5.79457$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
✓ |
$3, 5$ |
3B.1.1, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$338.7356671$ |
0.580410711 |
\( 3515 a^{3} - 3515 a^{2} - 21090 a - 11203 \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( a^{2} - 2 a - 1\) , \( -a^{2} + 2 a + 2\) , \( 2 a^{3} - 4 a^{2} - 6 a + 3\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+1\right){x}^{2}+\left(-a^{2}+2a+2\right){x}+2a^{3}-4a^{2}-6a+3$ |
| 7.1-a1 |
7.1-a |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{10} \) |
$7.39024$ |
$(-a^3+2a^2+3a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$153.0028475$ |
1.179740578 |
\( -\frac{30631833226798148}{282475249} a^{3} + \frac{19913145044553620}{282475249} a^{2} + \frac{160003945294303955}{282475249} a + \frac{86891270576754902}{282475249} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{2} - 3 a - 3\) , \( 0\) , \( 8 a^{3} - 16 a^{2} - 20 a - 4\) , \( 24 a^{3} - 80 a^{2} + 14 a + 49\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(8a^{3}-16a^{2}-20a-4\right){x}+24a^{3}-80a^{2}+14a+49$ |
| 7.1-a2 |
7.1-a |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{5} \) |
$7.39024$ |
$(-a^3+2a^2+3a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$306.0056951$ |
1.179740578 |
\( \frac{883009024}{16807} a^{3} - \frac{1375719561}{16807} a^{2} - \frac{3570496060}{16807} a + \frac{1021377428}{16807} \) |
\( \bigl[a^{2} - a - 1\) , \( a^{2} - 3 a - 3\) , \( 0\) , \( -2 a^{3} + 4 a^{2} + 5 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}={x}^{3}+\left(a^{2}-3a-3\right){x}^{2}+\left(-2a^{3}+4a^{2}+5a+1\right){x}$ |
| 7.1-a3 |
7.1-a |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{2} \) |
$7.39024$ |
$(-a^3+2a^2+3a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$153.0028475$ |
1.179740578 |
\( \frac{40225241338678555}{49} a^{3} + \frac{74036012651745535}{49} a^{2} + \frac{9175766779869835}{49} a - \frac{14161143749601521}{49} \) |
\( \bigl[a + 1\) , \( -2 a^{3} + 3 a^{2} + 8 a\) , \( a\) , \( 10 a^{3} - 21 a^{2} - 23 a - 1\) , \( -7 a^{3} + 31 a^{2} - 28 a - 32\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-2a^{3}+3a^{2}+8a\right){x}^{2}+\left(10a^{3}-21a^{2}-23a-1\right){x}-7a^{3}+31a^{2}-28a-32$ |
| 7.1-a4 |
7.1-a |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( -7 \) |
$7.39024$ |
$(-a^3+2a^2+3a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$306.0056951$ |
1.179740578 |
\( \frac{2677817}{7} a^{3} - \frac{117781460}{7} a^{2} - \frac{145844186}{7} a + \frac{65824690}{7} \) |
\( \bigl[a + 1\) , \( -2 a^{3} + 3 a^{2} + 8 a\) , \( a\) , \( -a^{2} + 2 a + 4\) , \( 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-2a^{3}+3a^{2}+8a\right){x}^{2}+\left(-a^{2}+2a+4\right){x}+1$ |
| 7.2-a1 |
7.2-a |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{10} \) |
$7.39024$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$153.0028475$ |
1.179740578 |
\( \frac{3873909021931313}{282475249} a^{3} + \frac{6844779160313215}{282475249} a^{2} + \frac{543599934897055}{282475249} a - \frac{1207912583197199}{282475249} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -17 a^{3} + 28 a^{2} + 65 a - 28\) , \( -39 a^{3} + 66 a^{2} + 150 a - 70\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a\right){x}^{2}+\left(-17a^{3}+28a^{2}+65a-28\right){x}-39a^{3}+66a^{2}+150a-70$ |
| 7.2-a2 |
7.2-a |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{5} \) |
$7.39024$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$306.0056951$ |
1.179740578 |
\( -\frac{351838523}{16807} a^{3} + \frac{844549060}{16807} a^{2} + \frac{383473054}{16807} a - \frac{207327710}{16807} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -2 a^{3} + 3 a^{2} + 10 a + 2\) , \( -a^{3} + 2 a^{2} + 5 a - 1\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+4a\right){x}^{2}+\left(-2a^{3}+3a^{2}+10a+2\right){x}-a^{3}+2a^{2}+5a-1$ |
| 7.2-a3 |
7.2-a |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{2} \) |
$7.39024$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \) |
$1$ |
$153.0028475$ |
1.179740578 |
\( -\frac{324563227463686700}{49} a^{3} + \frac{210301973473262610}{49} a^{2} + \frac{1696852149970179035}{49} a + \frac{921933595004884184}{49} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( -a^{2} + 3 a + 3\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -17 a^{3} + 28 a^{2} + 64 a - 29\) , \( 39 a^{3} - 63 a^{2} - 164 a + 42\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(-a^{2}+3a+3\right){x}^{2}+\left(-17a^{3}+28a^{2}+64a-29\right){x}+39a^{3}-63a^{2}-164a+42$ |
| 7.2-a4 |
7.2-a |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( -7 \) |
$7.39024$ |
$(a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$306.0056951$ |
1.179740578 |
\( \frac{247558744}{7} a^{3} - \frac{132455101}{7} a^{2} - \frac{1355575180}{7} a - \frac{754574452}{7} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( -a^{2} + 3 a + 3\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -2 a^{3} + 3 a^{2} + 9 a + 1\) , \( 1\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(a^{3}-a^{2}-5a-1\right){y}={x}^{3}+\left(-a^{2}+3a+3\right){x}^{2}+\left(-2a^{3}+3a^{2}+9a+1\right){x}+1$ |
| 13.1-a1 |
13.1-a |
$2$ |
$5$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
13.1 |
\( 13 \) |
\( 13 \) |
$7.98481$ |
$(a^3-a^2-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$0.027075662$ |
$830.3420360$ |
1.386797663 |
\( \frac{975752094999}{13} a^{3} - \frac{2483848785798}{13} a^{2} - \frac{1039789609026}{13} a + \frac{631320183976}{13} \) |
\( \bigl[a^{2} - 2 a - 1\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( a^{2} - a - 2\) , \( a^{3} - a^{2} - 3 a\) , \( -a^{2} - 2 a - 1\bigr] \) |
${y}^2+\left(a^{2}-2a-1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+1\right){x}^{2}+\left(a^{3}-a^{2}-3a\right){x}-a^{2}-2a-1$ |
| 13.1-a2 |
13.1-a |
$2$ |
$5$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
13.1 |
\( 13 \) |
\( 13^{5} \) |
$7.98481$ |
$(a^3-a^2-3a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 5 \) |
$0.005415132$ |
$830.3420360$ |
1.386797663 |
\( \frac{1603174098}{371293} a^{3} - \frac{7047580881}{371293} a^{2} - \frac{21430130708}{371293} a - \frac{10367581158}{371293} \) |
\( \bigl[a^{2} - a - 1\) , \( -a - 1\) , \( a^{2} - 2 a - 1\) , \( 2 a^{3} - 4 a^{2} - 7 a + 2\) , \( -2 a^{3} + 3 a^{2} + 9 a - 4\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a^{3}-4a^{2}-7a+2\right){x}-2a^{3}+3a^{2}+9a-4$ |
| 13.2-a1 |
13.2-a |
$2$ |
$5$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
13.2 |
\( 13 \) |
\( 13^{5} \) |
$7.98481$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 5 \) |
$0.005415132$ |
$830.3420360$ |
1.386797663 |
\( \frac{18858667001}{371293} a^{3} - \frac{13414260218}{371293} a^{2} - \frac{101340915886}{371293} a - \frac{54845107976}{371293} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -2 a\) , \( a^{3} - 3 a^{2} - a + 1\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(-a^{3}+2a^{2}+4a-1\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+1\right){x}^{2}-2a{x}+a^{3}-3a^{2}-a+1$ |
| 13.2-a2 |
13.2-a |
$2$ |
$5$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
13.2 |
\( 13 \) |
\( 13 \) |
$7.98481$ |
$(a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$0.027075662$ |
$830.3420360$ |
1.386797663 |
\( -\frac{2330874175170}{13} a^{3} + \frac{3838970865969}{13} a^{2} + \frac{9170522090052}{13} a - \frac{3602536999850}{13} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 1\) , \( a^{3} - a^{2} - 6 a - 1\) , \( a^{2} - a - 1\) , \( -a^{3} - a^{2} + 6 a + 7\) , \( 3 a^{3} - 3 a^{2} - 15 a - 7\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(a^{3}-a^{2}-6a-1\right){x}^{2}+\left(-a^{3}-a^{2}+6a+7\right){x}+3a^{3}-3a^{2}-15a-7$ |
| 16.1-a1 |
16.1-a |
$2$ |
$5$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{16} \) |
$8.19477$ |
$(2)$ |
$1$ |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.1 |
$1$ |
\( 2^{2} \) |
$0.072335044$ |
$2382.403286$ |
1.700830398 |
\( -\frac{1030301}{16} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a\) , \( a\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -a^{2} + 2 a - 1\) , \( -a^{3} + 2 a^{2} + 2 a - 1\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a\right){x}{y}+\left(-a^{3}+2a^{2}+4a-1\right){y}={x}^{3}+a{x}^{2}+\left(-a^{2}+2a-1\right){x}-a^{3}+2a^{2}+2a-1$ |
| 16.1-a2 |
16.1-a |
$2$ |
$5$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{80} \) |
$8.19477$ |
$(2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5B.1.2 |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.361675224$ |
$3.811845257$ |
1.700830398 |
\( \frac{237176659}{1048576} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a\) , \( a\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( 14 a^{2} + 2 a - 1\) , \( -a^{3} - 88 a^{2} - 13 a + 14\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a\right){x}{y}+\left(-a^{3}+2a^{2}+4a-1\right){y}={x}^{3}+a{x}^{2}+\left(14a^{2}+2a-1\right){x}-a^{3}-88a^{2}-13a+14$ |
| 23.1-a1 |
23.1-a |
$2$ |
$2$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$8.57507$ |
$(a^3-a^2-4a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$408.0392260$ |
1.573109391 |
\( -\frac{1397332}{23} a^{3} + \frac{2285752}{23} a^{2} + \frac{5502708}{23} a - \frac{2114405}{23} \) |
\( \bigl[a^{2} - a - 2\) , \( a - 1\) , \( a^{3} - a^{2} - 4 a\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -1\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a^{3}-a^{2}-5a-1\right){x}-1$ |
| 23.1-a2 |
23.1-a |
$2$ |
$2$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{2} \) |
$8.57507$ |
$(a^3-a^2-4a-4)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$204.0196130$ |
1.573109391 |
\( \frac{6062083940624}{529} a^{3} - \frac{9983678356718}{529} a^{2} - \frac{23849750535436}{529} a + \frac{9369060434537}{529} \) |
\( \bigl[a^{2} - a - 2\) , \( a - 1\) , \( a^{3} - a^{2} - 4 a\) , \( a^{3} - 6 a^{2} + 4\) , \( 2 a^{3} - 4 a^{2} - 2 a\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a^{3}-6a^{2}+4\right){x}+2a^{3}-4a^{2}-2a$ |
| 23.1-b1 |
23.1-b |
$2$ |
$5$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( - 23^{5} \) |
$8.57507$ |
$(a^3-a^2-4a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$101.1158007$ |
1.559322786 |
\( \frac{19544770289664}{6436343} a^{3} - \frac{49760136241152}{6436343} a^{2} - \frac{20811055325184}{6436343} a + \frac{12669824184320}{6436343} \) |
\( \bigl[0\) , \( 2 a^{3} - 3 a^{2} - 9 a - 1\) , \( a\) , \( a^{3} + 2 a + 5\) , \( -3 a^{2} - 4 a\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(2a^{3}-3a^{2}-9a-1\right){x}^{2}+\left(a^{3}+2a+5\right){x}-3a^{2}-4a$ |
| 23.1-b2 |
23.1-b |
$2$ |
$5$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$8.57507$ |
$(a^3-a^2-4a-4)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$101.1158007$ |
1.559322786 |
\( -\frac{131224616960}{23} a^{3} + \frac{85170323456}{23} a^{2} + \frac{685859135488}{23} a + \frac{372101771264}{23} \) |
\( \bigl[0\) , \( a^{3} - 2 a^{2} - 3 a\) , \( 1\) , \( -11 a^{3} - 14 a^{2} + a + 2\) , \( -63 a^{3} - 120 a^{2} - 16 a + 23\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a^{3}-2a^{2}-3a\right){x}^{2}+\left(-11a^{3}-14a^{2}+a+2\right){x}-63a^{3}-120a^{2}-16a+23$ |
| 23.1-c1 |
23.1-c |
$1$ |
$1$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
23.1 |
\( 23 \) |
\( -23 \) |
$8.57507$ |
$(a^3-a^2-4a-4)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.044062030$ |
$616.4016369$ |
1.675348968 |
\( \frac{327680}{23} a^{3} - \frac{925696}{23} a^{2} - \frac{339968}{23} a + \frac{262144}{23} \) |
\( \bigl[0\) , \( -2 a^{3} + 3 a^{2} + 9 a + 1\) , \( 1\) , \( -a^{2} + 2 a + 6\) , \( -2 a^{3} + 2 a^{2} + 8 a\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a+1\right){x}^{2}+\left(-a^{2}+2a+6\right){x}-2a^{3}+2a^{2}+8a$ |
| 23.2-a1 |
23.2-a |
$2$ |
$2$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$8.57507$ |
$(a^3-2a^2-5a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$408.0392260$ |
1.573109391 |
\( \frac{595532}{23} a^{3} - \frac{1483952}{23} a^{2} - \frac{691908}{23} a + \frac{334831}{23} \) |
\( \bigl[a^{2} - a - 1\) , \( 2 a^{3} - 3 a^{2} - 9 a - 1\) , \( 0\) , \( -a^{2} + a + 4\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-a-1\right){x}{y}={x}^{3}+\left(2a^{3}-3a^{2}-9a-1\right){x}^{2}+\left(-a^{2}+a+4\right){x}$ |
| 23.2-a2 |
23.2-a |
$2$ |
$2$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( - 23^{2} \) |
$8.57507$ |
$(a^3-2a^2-5a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$204.0196130$ |
1.573109391 |
\( -\frac{2539074751590}{529} a^{3} + \frac{6460669167684}{529} a^{2} + \frac{2711695401232}{529} a - \frac{1637752953719}{529} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( -a - 1\) , \( 0\) , \( 8 a^{3} + 16 a^{2} + 4 a - 4\) , \( -32 a^{3} - 57 a^{2} - 4 a + 10\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(8a^{3}+16a^{2}+4a-4\right){x}-32a^{3}-57a^{2}-4a+10$ |
| 23.2-b1 |
23.2-b |
$2$ |
$5$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( - 23^{5} \) |
$8.57507$ |
$(a^3-2a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$101.1158007$ |
1.559322786 |
\( -\frac{46697430171648}{6436343} a^{3} + \frac{76912796123136}{6436343} a^{2} + \frac{183727014617088}{6436343} a - \frac{72164805111808}{6436343} \) |
\( \bigl[0\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( a^{2} - 2 a - 2\) , \( -2 a^{3} - a^{2} + 1\) , \( 3 a^{3} + a^{2} - 2 a - 1\bigr] \) |
${y}^2+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(a^{3}-2a^{2}-2a+2\right){x}^{2}+\left(-2a^{3}-a^{2}+1\right){x}+3a^{3}+a^{2}-2a-1$ |
| 23.2-b2 |
23.2-b |
$2$ |
$5$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$8.57507$ |
$(a^3-2a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$101.1158007$ |
1.559322786 |
\( \frac{16318242816}{23} a^{3} + \frac{29736050688}{23} a^{2} + \frac{3579109376}{23} a - \frac{5712556032}{23} \) |
\( \bigl[0\) , \( -a^{3} + a^{2} + 5 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( a^{3} - 5 a^{2} - 3 a + 1\) , \( -a^{3} - a^{2} - 10 a - 7\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+2\right){x}^{2}+\left(a^{3}-5a^{2}-3a+1\right){x}-a^{3}-a^{2}-10a-7$ |
| 23.2-c1 |
23.2-c |
$1$ |
$1$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
23.2 |
\( 23 \) |
\( -23 \) |
$8.57507$ |
$(a^3-2a^2-5a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$0.044062030$ |
$616.4016369$ |
1.675348968 |
\( -\frac{700416}{23} a^{3} + \frac{1298432}{23} a^{2} + \frac{2576384}{23} a - \frac{1699840}{23} \) |
\( \bigl[0\) , \( -a^{2} + 3 a + 1\) , \( 1\) , \( -a^{3} + 4 a^{2} - 2 a - 3\) , \( 3 a^{3} - 5 a^{2} - 9 a - 3\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a^{2}+3a+1\right){x}^{2}+\left(-a^{3}+4a^{2}-2a-3\right){x}+3a^{3}-5a^{2}-9a-3$ |
| 25.1-a1 |
25.1-a |
$4$ |
$15$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$8.66491$ |
$(a^3-a^2-5a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B.1.1 |
$9$ |
\( 1 \) |
$1$ |
$166.6606862$ |
0.925236307 |
\( -1407628760845 a^{3} + 1407628760845 a^{2} + 8445772565070 a - 3086342051803 \) |
\( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - 2 a^{2} - 2 a + 2\) , \( 1\) , \( 19 a^{3} - 44 a^{2} - 39 a\) , \( -12 a^{3} + 116 a^{2} - 392 a - 305\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a-1\right){x}{y}+{y}={x}^{3}+\left(a^{3}-2a^{2}-2a+2\right){x}^{2}+\left(19a^{3}-44a^{2}-39a\right){x}-12a^{3}+116a^{2}-392a-305$ |
| 25.1-a2 |
25.1-a |
$4$ |
$15$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$8.66491$ |
$(a^3-a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$59.99784706$ |
0.925236307 |
\( 3515 a^{3} - 3515 a^{2} - 21090 a - 11203 \) |
\( \bigl[-a^{3} + 2 a^{2} + 3 a - 1\) , \( -2 a^{3} + 3 a^{2} + 9 a - 1\) , \( a^{2} - a - 1\) , \( 6 a^{3} - 6 a^{2} - 28 a - 8\) , \( 12 a^{3} - 10 a^{2} - 58 a - 33\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+3a-1\right){x}{y}+\left(a^{2}-a-1\right){y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a-1\right){x}^{2}+\left(6a^{3}-6a^{2}-28a-8\right){x}+12a^{3}-10a^{2}-58a-33$ |
| 25.1-a3 |
25.1-a |
$4$ |
$15$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$8.66491$ |
$(a^3-a^2-5a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1499.946176$ |
0.925236307 |
\( -3515 a^{3} + 3515 a^{2} + 21090 a - 7688 \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 1\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( a\) , \( -5 a^{3} + 9 a^{2} + 20 a - 8\) , \( 12 a^{3} - 19 a^{2} - 46 a + 18\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-1\right){x}{y}+a{y}={x}^{3}+\left(-a^{3}+2a^{2}+4a-2\right){x}^{2}+\left(-5a^{3}+9a^{2}+20a-8\right){x}+12a^{3}-19a^{2}-46a+18$ |
| 25.1-a4 |
25.1-a |
$4$ |
$15$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.1 |
\( 5^{2} \) |
\( 5^{6} \) |
$8.66491$ |
$(a^3-a^2-5a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$3, 5$ |
3B, 5B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$6.666427451$ |
0.925236307 |
\( 1407628760845 a^{3} - 1407628760845 a^{2} - 8445772565070 a - 4493970812648 \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a - 1\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( 18 a^{3} - 41 a^{2} - 40 a - 5\) , \( -519 a^{3} + 1336 a^{2} + 482 a - 388\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a-1\right){x}{y}+\left(-a^{3}+2a^{2}+3a\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a+1\right){x}^{2}+\left(18a^{3}-41a^{2}-40a-5\right){x}-519a^{3}+1336a^{2}+482a-388$ |
| 25.2-a1 |
25.2-a |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$454.8946779$ |
1.753750728 |
\( \frac{65131510848}{5} a^{3} - \frac{117013324586}{5} a^{2} - \frac{243658510307}{5} a + 28698510854 \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -9 a^{3} - 33 a^{2} - 21 a + 7\) , \( -91 a^{3} - 175 a^{2} - 36 a + 28\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(-a^{3}+2a^{2}+4a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+2\right){x}^{2}+\left(-9a^{3}-33a^{2}-21a+7\right){x}-91a^{3}-175a^{2}-36a+28$ |
| 25.2-a2 |
25.2-a |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{4} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$4$ |
\( 2 \) |
$1$ |
$56.86183474$ |
1.753750728 |
\( \frac{3513329359225657721383}{5} a^{3} - \frac{28932427283661365671972}{25} a^{2} - \frac{69113689989463250458806}{25} a + \frac{27150540167338724956708}{25} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -214 a^{3} - 388 a^{2} - 41 a + 67\) , \( -7172 a^{3} - 13212 a^{2} - 1656 a + 2523\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(-a^{3}+2a^{2}+4a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-4a+2\right){x}^{2}+\left(-214a^{3}-388a^{2}-41a+67\right){x}-7172a^{3}-13212a^{2}-1656a+2523$ |
| 25.2-a3 |
25.2-a |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{20} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$4$ |
\( 2 \) |
$1$ |
$56.86183474$ |
1.753750728 |
\( -\frac{22468935090080842}{9765625} a^{3} + \frac{57196470894762219}{9765625} a^{2} + \frac{23943427807517778}{9765625} a - \frac{2907514221294602}{1953125} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 5 a\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -12 a^{3} + 8 a^{2} + 77 a - 17\) , \( 95 a^{3} - 189 a^{2} - 282 a + 147\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{3}+2a^{2}+4a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(-12a^{3}+8a^{2}+77a-17\right){x}+95a^{3}-189a^{2}-282a+147$ |
| 25.2-a4 |
25.2-a |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$454.8946779$ |
1.753750728 |
\( \frac{119956585901}{625} a^{3} + \frac{1104160687393}{3125} a^{2} + \frac{136893951569}{3125} a - \frac{211188734797}{3125} \) |
\( \bigl[a\) , \( -a^{3} + a^{2} + 5 a\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -2 a^{3} + 3 a^{2} + 7 a - 7\) , \( -a^{3} + a^{2} + 5 a - 1\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{3}+2a^{2}+4a-1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a\right){x}^{2}+\left(-2a^{3}+3a^{2}+7a-7\right){x}-a^{3}+a^{2}+5a-1$ |
| 25.2-b1 |
25.2-b |
$4$ |
$6$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1.450114568$ |
$9.444482440$ |
1.900815604 |
\( -\frac{455036091959024}{5} a^{3} + \frac{1511067971488404}{5} a^{2} + \frac{588945358269284}{5} a - \frac{374758642631459}{5} \) |
\( \bigl[a\) , \( a^{3} - 2 a^{2} - 3 a\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( -166 a^{3} + 251 a^{2} + 628 a - 250\) , \( -1268 a^{3} + 1952 a^{2} + 4830 a - 1890\bigr] \) |
${y}^2+a{x}{y}+\left(-a^{3}+2a^{2}+3a\right){y}={x}^{3}+\left(a^{3}-2a^{2}-3a\right){x}^{2}+\left(-166a^{3}+251a^{2}+628a-250\right){x}-1268a^{3}+1952a^{2}+4830a-1890$ |
| 25.2-b2 |
25.2-b |
$4$ |
$6$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{12} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.966743045$ |
$191.2507694$ |
1.900815604 |
\( \frac{2913650591998}{15625} a^{3} + \frac{5477243309467}{15625} a^{2} + \frac{915780952932}{15625} a - \frac{911209721057}{15625} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a\) , \( -2 a^{3} + 3 a^{2} + 9 a + 1\) , \( 1\) , \( 35 a^{3} - 33 a^{2} - 152 a - 73\) , \( -81 a^{3} + 54 a^{2} + 430 a + 234\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a\right){x}{y}+{y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a+1\right){x}^{2}+\left(35a^{3}-33a^{2}-152a-73\right){x}-81a^{3}+54a^{2}+430a+234$ |
| 25.2-b3 |
25.2-b |
$4$ |
$6$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.483371522$ |
$765.0030776$ |
1.900815604 |
\( \frac{39799849}{125} a^{3} - \frac{63283589}{125} a^{2} - \frac{159749839}{125} a + \frac{62911724}{125} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a\) , \( -2 a^{3} + 3 a^{2} + 9 a + 1\) , \( 1\) , \( 5 a^{3} - 8 a^{2} - 7 a + 2\) , \( 12 a^{3} - 25 a^{2} - 14 a + 5\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a\right){x}{y}+{y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a+1\right){x}^{2}+\left(5a^{3}-8a^{2}-7a+2\right){x}+12a^{3}-25a^{2}-14a+5$ |
| 25.2-b4 |
25.2-b |
$4$ |
$6$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{4} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$2.900229137$ |
$2.361120610$ |
1.900815604 |
\( \frac{246199023533429793802832076808}{25} a^{3} + \frac{453138213764112525371698488272}{25} a^{2} + \frac{56160379457348258811003590942}{25} a - \frac{86673433010725415101151339157}{25} \) |
\( \bigl[-a^{3} + 2 a^{2} + 4 a\) , \( -2 a^{3} + 3 a^{2} + 9 a + 1\) , \( 1\) , \( 345 a^{3} - 773 a^{2} - 617 a + 27\) , \( 5642 a^{3} - 13899 a^{2} - 7188 a + 2678\bigr] \) |
${y}^2+\left(-a^{3}+2a^{2}+4a\right){x}{y}+{y}={x}^{3}+\left(-2a^{3}+3a^{2}+9a+1\right){x}^{2}+\left(345a^{3}-773a^{2}-617a+27\right){x}+5642a^{3}-13899a^{2}-7188a+2678$ |
| 25.2-c1 |
25.2-c |
$4$ |
$6$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{4} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 2 \) |
$2.900229137$ |
$2.361120610$ |
1.900815604 |
\( -\frac{1986492734422039546999694540062}{25} a^{3} + \frac{1287155497124497227825163974982}{25} a^{2} + \frac{10385601885874310260370171188582}{25} a + \frac{5642704511432455521574028103113}{25} \) |
\( \bigl[a^{2} - 2 a - 2\) , \( a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( -674 a^{3} + 1104 a^{2} + 2595 a - 1107\) , \( -11941 a^{3} + 19624 a^{2} + 46771 a - 18677\bigr] \) |
${y}^2+\left(a^{2}-2a-2\right){x}{y}+\left(-a^{3}+2a^{2}+3a\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-674a^{3}+1104a^{2}+2595a-1107\right){x}-11941a^{3}+19624a^{2}+46771a-18677$ |
| 25.2-c2 |
25.2-c |
$4$ |
$6$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{12} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.966743045$ |
$191.2507694$ |
1.900815604 |
\( -\frac{23874927814387}{15625} a^{3} + \frac{15484033912922}{15625} a^{2} + \frac{124851882381402}{15625} a + \frac{67831838192653}{15625} \) |
\( \bigl[a^{2} - 2 a - 2\) , \( a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( -19 a^{3} + 19 a^{2} + 60 a - 22\) , \( 31 a^{3} - 8 a^{2} - 71 a + 24\bigr] \) |
${y}^2+\left(a^{2}-2a-2\right){x}{y}+\left(-a^{3}+2a^{2}+3a\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-19a^{3}+19a^{2}+60a-22\right){x}+31a^{3}-8a^{2}-71a+24$ |
| 25.2-c3 |
25.2-c |
$4$ |
$6$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{6} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.483371522$ |
$765.0030776$ |
1.900815604 |
\( -\frac{15765666}{125} a^{3} + \frac{39249406}{125} a^{2} + \frac{15544741}{125} a + \frac{1058539}{125} \) |
\( \bigl[a^{2} - 2 a - 2\) , \( a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( -9 a^{3} + 14 a^{2} + 35 a - 12\) , \( -14 a^{3} + 23 a^{2} + 55 a - 22\bigr] \) |
${y}^2+\left(a^{2}-2a-2\right){x}{y}+\left(-a^{3}+2a^{2}+3a\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-9a^{3}+14a^{2}+35a-12\right){x}-14a^{3}+23a^{2}+55a-22$ |
| 25.2-c4 |
25.2-c |
$4$ |
$6$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$9$ |
\( 1 \) |
$1.450114568$ |
$9.444482440$ |
1.900815604 |
\( \frac{630203221996456}{5} a^{3} - \frac{1686235101525836}{5} a^{2} - \frac{1639948138493876}{5} a + \frac{3820161441059961}{5} \) |
\( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a\) , \( a^{2} - 2 a - 2\) , \( 114 a^{3} - 197 a^{2} - 323 a - 110\) , \( 942 a^{3} - 1711 a^{2} - 2507 a - 671\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a-1\right){x}{y}+\left(a^{2}-2a-2\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a\right){x}^{2}+\left(114a^{3}-197a^{2}-323a-110\right){x}+942a^{3}-1711a^{2}-2507a-671$ |
| 25.2-d1 |
25.2-d |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{4} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$4$ |
\( 2 \) |
$1$ |
$56.86183474$ |
1.753750728 |
\( -\frac{7353763503645115510712}{25} a^{3} + \frac{18719543991178192575769}{25} a^{2} + \frac{7836390234564211881588}{25} a - 190318078822130250038 \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( 0\) , \( 30 a^{3} - 79 a^{2} - 151 a - 56\) , \( -44 a^{3} - 121 a^{2} - 736 a - 437\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+6a+1\right){x}^{2}+\left(30a^{3}-79a^{2}-151a-56\right){x}-44a^{3}-121a^{2}-736a-437$ |
| 25.2-d2 |
25.2-d |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{2} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 1 \) |
$1$ |
$454.8946779$ |
1.753750728 |
\( -6023446039 a^{3} + \frac{81999043933}{5} a^{2} + \frac{33572826389}{5} a - \frac{20667773377}{5} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( 0\) , \( -10 a^{3} - 24 a^{2} - 6 a + 4\) , \( -116 a^{3} - 216 a^{2} - 44 a + 31\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}={x}^{3}+\left(-a^{3}+a^{2}+6a+1\right){x}^{2}+\left(-10a^{3}-24a^{2}-6a+4\right){x}-116a^{3}-216a^{2}-44a+31$ |
| 25.2-d3 |
25.2-d |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( - 5^{20} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$4$ |
\( 2 \) |
$1$ |
$56.86183474$ |
1.753750728 |
\( \frac{10734742367641011}{1953125} a^{3} - \frac{88401247642886432}{9765625} a^{2} - \frac{211172088296263056}{9765625} a + \frac{82957460988647978}{9765625} \) |
\( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( a - 1\) , \( a^{2} - 2 a - 1\) , \( -14 a^{3} + 18 a^{2} + 78 a - 35\) , \( -99 a^{3} + 192 a^{2} + 308 a - 127\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a-1\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-14a^{3}+18a^{2}+78a-35\right){x}-99a^{3}+192a^{2}+308a-127$ |
| 25.2-d4 |
25.2-d |
$4$ |
$10$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
25.2 |
\( 5^{2} \) |
\( 5^{10} \) |
$8.66491$ |
$(-2a^3+3a^2+8a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$454.8946779$ |
1.753750728 |
\( -\frac{4839752215992}{3125} a^{3} + \frac{3135808599094}{3125} a^{2} + \frac{25302921767353}{3125} a + \frac{2749612899038}{625} \) |
\( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( a - 1\) , \( a^{2} - 2 a - 1\) , \( a^{3} - 2 a^{2} - 2 a - 5\) , \( -a^{2} + 3 a\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a-1\right){x}{y}+\left(a^{2}-2a-1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(a^{3}-2a^{2}-2a-5\right){x}-a^{2}+3a$ |
| 35.1-a1 |
35.1-a |
$2$ |
$2$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( - 5^{4} \cdot 7 \) |
$9.03712$ |
$(a^3-a^2-5a), (a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$176.7293811$ |
1.362685896 |
\( -\frac{5455613}{175} a^{3} - \frac{7906721}{175} a^{2} + \frac{1037279}{175} a + \frac{712897}{175} \) |
\( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( a^{3} - a^{2} - 4 a\) , \( -3 a - 2\) , \( -a^{3} + 2 a\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-4a-1\right){x}{y}+\left(a^{3}-a^{2}-4a\right){y}={x}^{3}+\left(-a^{3}+2a^{2}+3a-1\right){x}^{2}+\left(-3a-2\right){x}-a^{3}+2a$ |
| 35.1-a2 |
35.1-a |
$2$ |
$2$ |
4.4.4205.1 |
$4$ |
$[4, 0]$ |
35.1 |
\( 5 \cdot 7 \) |
\( - 5^{2} \cdot 7^{2} \) |
$9.03712$ |
$(a^3-a^2-5a), (a^2-2a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$88.36469059$ |
1.362685896 |
\( \frac{7225917770032}{245} a^{3} + \frac{13267053439387}{245} a^{2} + \frac{1609758798882}{245} a - \frac{505153678396}{49} \) |
\( \bigl[a^{3} - a^{2} - 5 a\) , \( -a^{2} + 2 a + 1\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -31 a^{3} + 56 a^{2} + 110 a - 55\) , \( -129 a^{3} + 209 a^{2} + 514 a - 193\bigr] \) |
${y}^2+\left(a^{3}-a^{2}-5a\right){x}{y}+\left(-a^{3}+2a^{2}+4a-1\right){y}={x}^{3}+\left(-a^{2}+2a+1\right){x}^{2}+\left(-31a^{3}+56a^{2}+110a-55\right){x}-129a^{3}+209a^{2}+514a-193$ |
*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.
