| 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 |
$2$ |
$5$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.75779$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$5$ |
5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$6.245544858$ |
1.798502654 |
\( -334965626056392215625 a^{3} - 388478312623870931247 a^{2} + 835809858812480343750 a + 465282648622016250736 \) |
\( \bigl[a + 1\) , \( a\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 178 a^{3} - 268 a^{2} - 758 a + 1094\) , \( 947812 a^{3} - 1414058 a^{2} - 4043459 a + 5780296\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+a{x}^{2}+\left(178a^{3}-268a^{2}-758a+1094\right){x}+947812a^{3}-1414058a^{2}-4043459a+5780296$ |
| 1.1-a2 |
1.1-a |
$2$ |
$5$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.75779$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$156.1386214$ |
1.798502654 |
\( -3312 a^{3} - 831 a^{2} + 10224 a - 3737 \) |
\( \bigl[a + 1\) , \( -a^{3} + 4 a\) , \( a^{3} - 3 a + 1\) , \( -3 a^{3} - 2 a^{2} + 11 a + 6\) , \( -a^{3} - a^{2} + 3 a\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(-3a^{3}-2a^{2}+11a+6\right){x}-a^{3}-a^{2}+3a$ |
| 1.1-b1 |
1.1-b |
$2$ |
$5$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.75779$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$5$ |
5B.1.2 |
$25$ |
\( 1 \) |
$1$ |
$1.086096037$ |
0.312758398 |
\( -334965626056392215625 a^{3} - 388478312623870931247 a^{2} + 835809858812480343750 a + 465282648622016250736 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - a^{2} - 5 a + 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 19 a^{3} - 45 a^{2} - 44 a + 96\) , \( -17805 a^{3} + 26502 a^{2} + 76153 a - 108738\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+2\right){x}^{2}+\left(19a^{3}-45a^{2}-44a+96\right){x}-17805a^{3}+26502a^{2}+76153a-108738$ |
| 1.1-b2 |
1.1-b |
$2$ |
$5$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$7.75779$ |
$\textsf{none}$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$5$ |
5B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$678.8100232$ |
0.312758398 |
\( -3312 a^{3} - 831 a^{2} + 10224 a - 3737 \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{3} - a^{2} + 5 a + 4\) , \( a^{3} - 3 a + 1\) , \( -5 a^{3} - 3 a^{2} + 22 a + 16\) , \( -21 a^{3} - 8 a^{2} + 94 a + 45\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(-a^{3}-a^{2}+5a+4\right){x}^{2}+\left(-5a^{3}-3a^{2}+22a+16\right){x}-21a^{3}-8a^{2}+94a+45$ |
| 3.1-a1 |
3.1-a |
$4$ |
$4$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{12} \) |
$8.89975$ |
$(-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$53.36980872$ |
1.229493916 |
\( \frac{4190085756389728}{531441} a^{3} - \frac{6336022563666616}{531441} a^{2} - \frac{17865773841419786}{531441} a + \frac{25928282958304123}{531441} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + 2\) , \( a^{2} - 3\) , \( 37 a^{3} + 15 a^{2} - 165 a - 83\) , \( 194 a^{3} + 76 a^{2} - 869 a - 432\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(37a^{3}+15a^{2}-165a-83\right){x}+194a^{3}+76a^{2}-869a-432$ |
| 3.1-a2 |
3.1-a |
$4$ |
$4$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$8.89975$ |
$(-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$853.9169395$ |
1.229493916 |
\( -\frac{364894112}{729} a^{3} + \frac{1138392116}{729} a^{2} - \frac{563847836}{729} a - \frac{414942815}{729} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + 2\) , \( a^{2} - 3\) , \( 2 a^{3} - 10 a - 3\) , \( 3 a^{3} + a^{2} - 14 a - 6\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(2a^{3}-10a-3\right){x}+3a^{3}+a^{2}-14a-6$ |
| 3.1-a3 |
3.1-a |
$4$ |
$4$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{3} \) |
$8.89975$ |
$(-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$426.9584697$ |
1.229493916 |
\( -\frac{169180745246306}{27} a^{3} + \frac{515522689848500}{27} a^{2} - \frac{209459430134084}{27} a - \frac{247923703171943}{27} \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} + 4 a + 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -32 a^{3} + 20 a^{2} + 119 a - 114\) , \( -72 a^{3} - 111 a^{2} + 161 a + 177\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{3}+4a+1\right){x}^{2}+\left(-32a^{3}+20a^{2}+119a-114\right){x}-72a^{3}-111a^{2}+161a+177$ |
| 3.1-a4 |
3.1-a |
$4$ |
$4$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{3} \) |
$8.89975$ |
$(-a^3+a^2+4a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1707.833879$ |
1.229493916 |
\( \frac{427922}{27} a^{3} + \frac{498316}{27} a^{2} - \frac{1015990}{27} a - \frac{571303}{27} \) |
\( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 5 a + 2\) , \( a^{3} - 4 a + 1\) , \( a^{2} - 4\) , \( -9 a^{3} + 13 a^{2} + 38 a - 54\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+2\right){x}^{2}+\left(a^{2}-4\right){x}-9a^{3}+13a^{2}+38a-54$ |
| 3.1-b1 |
3.1-b |
$4$ |
$4$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{12} \) |
$8.89975$ |
$(-a^3+a^2+4a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.011935148$ |
$667.3441168$ |
1.100929835 |
\( \frac{4190085756389728}{531441} a^{3} - \frac{6336022563666616}{531441} a^{2} - \frac{17865773841419786}{531441} a + \frac{25928282958304123}{531441} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 5 a + 4\) , \( a^{2} - 2\) , \( 13 a^{3} - 4 a^{2} - 44 a - 7\) , \( -18 a^{3} + a^{2} + 64 a + 37\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+4\right){x}^{2}+\left(13a^{3}-4a^{2}-44a-7\right){x}-18a^{3}+a^{2}+64a+37$ |
| 3.1-b2 |
3.1-b |
$4$ |
$4$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{6} \) |
$8.89975$ |
$(-a^3+a^2+4a-3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \cdot 3 \) |
$0.023870296$ |
$2669.376467$ |
1.100929835 |
\( -\frac{364894112}{729} a^{3} + \frac{1138392116}{729} a^{2} - \frac{563847836}{729} a - \frac{414942815}{729} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 5 a + 4\) , \( a^{2} - 2\) , \( 3 a^{3} - 9 a^{2} - 4 a + 13\) , \( -3 a^{3} + 9 a^{2} - 8 a + 2\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-5a+4\right){x}^{2}+\left(3a^{3}-9a^{2}-4a+13\right){x}-3a^{3}+9a^{2}-8a+2$ |
| 3.1-b3 |
3.1-b |
$4$ |
$4$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( - 3^{3} \) |
$8.89975$ |
$(-a^3+a^2+4a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.047740592$ |
$667.3441168$ |
1.100929835 |
\( -\frac{169180745246306}{27} a^{3} + \frac{515522689848500}{27} a^{2} - \frac{209459430134084}{27} a - \frac{247923703171943}{27} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 4 a + 1\) , \( a + 1\) , \( -27 a^{3} - 31 a^{2} + 68 a + 37\) , \( -220 a^{3} - 250 a^{2} + 552 a + 290\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(-27a^{3}-31a^{2}+68a+37\right){x}-220a^{3}-250a^{2}+552a+290$ |
| 3.1-b4 |
3.1-b |
$4$ |
$4$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
3.1 |
\( 3 \) |
\( 3^{3} \) |
$8.89975$ |
$(-a^3+a^2+4a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.011935148$ |
$2669.376467$ |
1.100929835 |
\( \frac{427922}{27} a^{3} + \frac{498316}{27} a^{2} - \frac{1015990}{27} a - \frac{571303}{27} \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( a^{3} - 4 a\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( 0\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}-a^{2}+4a+3\right){x}^{2}+\left(-a^{3}-a^{2}+4a+4\right){x}$ |
| 6.1-a1 |
6.1-a |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{10} \cdot 3^{5} \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$491.7983524$ |
0.708105267 |
\( \frac{168007031423}{248832} a^{3} + \frac{102781155539}{124416} a^{2} - \frac{392025741433}{248832} a - \frac{222581913607}{248832} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a - 1\) , \( a^{3} - 3 a + 1\) , \( -3 a^{3} - a^{2} + 7 a + 5\) , \( a^{3} - 6 a^{2} + 6 a + 3\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-3a^{3}-a^{2}+7a+5\right){x}+a^{3}-6a^{2}+6a+3$ |
| 6.1-a2 |
6.1-a |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3 \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2 \) |
$1$ |
$19.67193409$ |
0.708105267 |
\( -\frac{3788224206297237403494187489}{12} a^{3} - \frac{718500734519060282578518727}{6} a^{2} + \frac{16959016340050334034144749999}{12} a + \frac{8239247562980311995990608885}{12} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a - 1\) , \( a^{3} - 3 a + 1\) , \( 227 a^{3} - 606 a^{2} + 67 a + 200\) , \( 4462 a^{3} - 15104 a^{2} + 7561 a + 7917\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-3a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(227a^{3}-606a^{2}+67a+200\right){x}+4462a^{3}-15104a^{2}+7561a+7917$ |
| 6.1-a3 |
6.1-a |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$25$ |
\( 2 \) |
$1$ |
$4.917983524$ |
0.708105267 |
\( \frac{684295128809102280000613}{768} a^{3} + \frac{396778102159617837600193}{384} a^{2} - \frac{1707500027171046981603011}{768} a - \frac{950350754797571713825469}{768} \) |
\( \bigl[a\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -1580 a^{3} - 1883 a^{2} + 21103 a - 21374\) , \( 535239 a^{3} - 1185664 a^{2} - 918954 a + 2118749\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(-1580a^{3}-1883a^{2}+21103a-21374\right){x}+535239a^{3}-1185664a^{2}-918954a+2118749$ |
| 6.1-a4 |
6.1-a |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{40} \cdot 3^{5} \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$122.9495881$ |
0.708105267 |
\( \frac{717911690213179189}{267181325549568} a^{3} + \frac{439260339852006865}{133590662774784} a^{2} - \frac{2122796805114383219}{267181325549568} a - \frac{165768284134898189}{267181325549568} \) |
\( \bigl[a\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 5 a^{3} - 38 a^{2} + 63 a - 14\) , \( -61 a^{3} + 219 a^{2} - 186 a - 10\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(5a^{3}-38a^{2}+63a-14\right){x}-61a^{3}+219a^{2}-186a-10$ |
| 6.1-a5 |
6.1-a |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.4.2 |
$25$ |
\( 2^{2} \) |
$1$ |
$9.835967049$ |
0.708105267 |
\( -\frac{475241186762663399945}{144} a^{3} + \frac{724068654623944874971}{72} a^{2} - \frac{588380431714959600209}{144} a - \frac{696431786649047441711}{144} \) |
\( \bigl[a\) , \( -a^{2} + a + 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 2444 a^{3} + 656 a^{2} - 11121 a - 5365\) , \( -115699 a^{3} - 47601 a^{2} + 513827 a + 250549\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(2444a^{3}+656a^{2}-11121a-5365\right){x}-115699a^{3}-47601a^{2}+513827a+250549$ |
| 6.1-a6 |
6.1-a |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{4} \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.2 |
$100$ |
\( 2^{2} \) |
$1$ |
$0.614747940$ |
0.708105267 |
\( -\frac{79115826550724905777967802178252157173769}{324} a^{3} + \frac{120539731137470646549210558717174946235821}{162} a^{2} - \frac{97951781487083673082391696384596503343085}{324} a - \frac{115939247402344735742019997951654169031299}{324} \) |
\( \bigl[a\) , \( -a^{2} + a + 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 2994 a^{3} - 1019 a^{2} - 10441 a - 4560\) , \( -90803 a^{3} - 123454 a^{2} + 544618 a + 287013\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(2994a^{3}-1019a^{2}-10441a-4560\right){x}-90803a^{3}-123454a^{2}+544618a+287013$ |
| 6.1-a7 |
6.1-a |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{10} \cdot 3^{20} \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.4.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$15.36869851$ |
0.708105267 |
\( \frac{163051863816287762155}{3570467226624} a^{3} - \frac{110850887870650240049}{1785233613312} a^{2} - \frac{773258527443007514477}{3570467226624} a + \frac{1061560648300939491565}{3570467226624} \) |
\( \bigl[a\) , \( -a^{2} + a + 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 69 a^{3} + 26 a^{2} - 301 a - 150\) , \( 527 a^{3} + 202 a^{2} - 2347 a - 1146\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(69a^{3}+26a^{2}-301a-150\right){x}+527a^{3}+202a^{2}-2347a-1146$ |
| 6.1-a8 |
6.1-a |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{20} \cdot 3^{10} \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.4.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$245.8991762$ |
0.708105267 |
\( \frac{137453854619383}{61917364224} a^{3} - \frac{69119317227029}{30958682112} a^{2} - \frac{694491025501121}{61917364224} a + \frac{967236366550849}{61917364224} \) |
\( \bigl[a\) , \( -a^{2} + a + 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 4 a^{3} + a^{2} - 21 a - 10\) , \( 5 a^{3} + 2 a^{2} - 22 a - 11\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(4a^{3}+a^{2}-21a-10\right){x}+5a^{3}+2a^{2}-22a-11$ |
| 6.1-b1 |
6.1-b |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{2} \cdot 3 \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2 \) |
$1$ |
$0.620829796$ |
2.234721032 |
\( -\frac{3788224206297237403494187489}{12} a^{3} - \frac{718500734519060282578518727}{6} a^{2} + \frac{16959016340050334034144749999}{12} a + \frac{8239247562980311995990608885}{12} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + 3 a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 218 a^{3} + 78 a^{2} - 961 a - 581\) , \( 3280 a^{3} + 1207 a^{2} - 14527 a - 7639\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(218a^{3}+78a^{2}-961a-581\right){x}+3280a^{3}+1207a^{2}-14527a-7639$ |
| 6.1-b2 |
6.1-b |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{10} \cdot 3^{5} \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2 \cdot 5^{2} \) |
$1$ |
$388.0186227$ |
2.234721032 |
\( \frac{168007031423}{248832} a^{3} + \frac{102781155539}{124416} a^{2} - \frac{392025741433}{248832} a - \frac{222581913607}{248832} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{3} + 3 a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -2 a^{3} - 2 a^{2} + 4 a + 4\) , \( -a^{2} - 2 a + 2\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a^{3}+3a+1\right){x}^{2}+\left(-2a^{3}-2a^{2}+4a+4\right){x}-a^{2}-2a+2$ |
| 6.1-b3 |
6.1-b |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{8} \cdot 3 \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2^{3} \) |
$1$ |
$0.155207449$ |
2.234721032 |
\( \frac{684295128809102280000613}{768} a^{3} + \frac{396778102159617837600193}{384} a^{2} - \frac{1707500027171046981603011}{768} a - \frac{950350754797571713825469}{768} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a + 1\) , \( -58525 a^{3} + 87116 a^{2} + 250157 a - 357243\) , \( -15155555 a^{3} + 22607689 a^{2} + 64664119 a - 92433752\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-58525a^{3}+87116a^{2}+250157a-357243\right){x}-15155555a^{3}+22607689a^{2}+64664119a-92433752$ |
| 6.1-b4 |
6.1-b |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{40} \cdot 3^{5} \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$97.00465569$ |
2.234721032 |
\( \frac{717911690213179189}{267181325549568} a^{3} + \frac{439260339852006865}{133590662774784} a^{2} - \frac{2122796805114383219}{267181325549568} a - \frac{165768284134898189}{267181325549568} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a + 1\) , \( -100 a^{3} + 151 a^{2} + 432 a - 618\) , \( -781 a^{3} + 1170 a^{2} + 3330 a - 4772\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(-100a^{3}+151a^{2}+432a-618\right){x}-781a^{3}+1170a^{2}+3330a-4772$ |
| 6.1-b5 |
6.1-b |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{2} \cdot 3^{4} \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.2 |
$625$ |
\( 2^{3} \) |
$1$ |
$0.155207449$ |
2.234721032 |
\( -\frac{79115826550724905777967802178252157173769}{324} a^{3} + \frac{120539731137470646549210558717174946235821}{162} a^{2} - \frac{97951781487083673082391696384596503343085}{324} a - \frac{115939247402344735742019997951654169031299}{324} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( a^{2} - 3\) , \( 11356 a^{3} + 4261 a^{2} - 50897 a - 25102\) , \( 1052279 a^{3} + 398317 a^{2} - 4711755 a - 2291461\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(11356a^{3}+4261a^{2}-50897a-25102\right){x}+1052279a^{3}+398317a^{2}-4711755a-2291461$ |
| 6.1-b6 |
6.1-b |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{20} \cdot 3^{10} \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$388.0186227$ |
2.234721032 |
\( \frac{137453854619383}{61917364224} a^{3} - \frac{69119317227029}{30958682112} a^{2} - \frac{694491025501121}{61917364224} a + \frac{967236366550849}{61917364224} \) |
\( \bigl[a^{2} - 2\) , \( a^{2} - 3\) , \( a^{2} - 3\) , \( 26 a^{3} + 11 a^{2} - 117 a - 62\) , \( -11 a^{3} - 5 a^{2} + 49 a + 27\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(26a^{3}+11a^{2}-117a-62\right){x}-11a^{3}-5a^{2}+49a+27$ |
| 6.1-b7 |
6.1-b |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( - 2^{10} \cdot 3^{20} \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/10\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2B, 5B.1.1 |
$1$ |
\( 2^{3} \cdot 5^{2} \) |
$1$ |
$97.00465569$ |
2.234721032 |
\( \frac{163051863816287762155}{3570467226624} a^{3} - \frac{110850887870650240049}{1785233613312} a^{2} - \frac{773258527443007514477}{3570467226624} a + \frac{1061560648300939491565}{3570467226624} \) |
\( \bigl[1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - 3\) , \( 47 a^{3} - 66 a^{2} - 51 a - 2\) , \( 189 a^{3} - 696 a^{2} + 512 a + 441\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(47a^{3}-66a^{2}-51a-2\right){x}+189a^{3}-696a^{2}+512a+441$ |
| 6.1-b8 |
6.1-b |
$8$ |
$20$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
6.1 |
\( 2 \cdot 3 \) |
\( 2^{4} \cdot 3^{2} \) |
$9.70525$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 5$ |
2Cs, 5B.1.2 |
$625$ |
\( 2^{3} \) |
$1$ |
$0.620829796$ |
2.234721032 |
\( -\frac{475241186762663399945}{144} a^{3} + \frac{724068654623944874971}{72} a^{2} - \frac{588380431714959600209}{144} a - \frac{696431786649047441711}{144} \) |
\( \bigl[1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - 3\) , \( 1157 a^{3} - 3351 a^{2} - 306 a + 798\) , \( 58381 a^{3} - 184721 a^{2} + 46364 a + 74454\bigr] \) |
${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-3a-3\right){x}^{2}+\left(1157a^{3}-3351a^{2}-306a+798\right){x}+58381a^{3}-184721a^{2}+46364a+74454$ |
| 8.1-a1 |
8.1-a |
$1$ |
$1$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$10.06060$ |
$(a^3-5a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2 \) |
$1$ |
$188.3644467$ |
4.339399878 |
\( \frac{697025}{16} a^{3} + \frac{64903}{4} a^{2} - \frac{390197}{2} a - \frac{1492455}{16} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{2} + 2\) , \( a^{2} + a - 3\) , \( 2 a^{3} - 3 a^{2} - 10 a + 11\) , \( a^{3} - a^{2} - 5 a + 2\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(2a^{3}-3a^{2}-10a+11\right){x}+a^{3}-a^{2}-5a+2$ |
| 8.1-b1 |
8.1-b |
$2$ |
$3$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$10.06060$ |
$(a^3-5a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
$9$ |
\( 2 \) |
$1$ |
$5.025231029$ |
1.041907778 |
\( -\frac{14994258421875}{64} a^{3} + \frac{22731472549625}{64} a^{2} + \frac{63926300861025}{64} a - \frac{93040847184083}{64} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 4\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 27 a^{2} + 13 a - 87\) , \( -1709 a^{3} - 1804 a^{2} + 4370 a + 1844\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(27a^{2}+13a-87\right){x}-1709a^{3}-1804a^{2}+4370a+1844$ |
| 8.1-b2 |
8.1-b |
$2$ |
$3$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$10.06060$ |
$(a^3-5a+1)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$407.0437133$ |
1.041907778 |
\( \frac{164503}{2} a^{3} - \frac{503437}{2} a^{2} + \frac{431925}{4} a + \frac{449257}{4} \) |
\( \bigl[a^{2} - 3\) , \( -a^{2} + 4\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -3 a^{2} - 2 a + 8\) , \( 62 a^{3} + 70 a^{2} - 157 a - 83\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-3a^{2}-2a+8\right){x}+62a^{3}+70a^{2}-157a-83$ |
| 8.1-c1 |
8.1-c |
$2$ |
$3$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{18} \) |
$10.06060$ |
$(a^3-5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.015513424$ |
$336.9560643$ |
1.445083487 |
\( -\frac{14994258421875}{64} a^{3} + \frac{22731472549625}{64} a^{2} + \frac{63926300861025}{64} a - \frac{93040847184083}{64} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 17 a^{3} + 22 a^{2} - 44 a - 31\) , \( -5598 a^{3} - 6493 a^{2} + 13967 a + 7779\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(17a^{3}+22a^{2}-44a-31\right){x}-5598a^{3}-6493a^{2}+13967a+7779$ |
| 8.1-c2 |
8.1-c |
$2$ |
$3$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{6} \) |
$10.06060$ |
$(a^3-5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.005171141$ |
$3032.604578$ |
1.445083487 |
\( \frac{164503}{2} a^{3} - \frac{503437}{2} a^{2} + \frac{431925}{4} a + \frac{449257}{4} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a + 1\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -3 a^{3} - 3 a^{2} + 6 a + 4\) , \( 205 a^{3} + 238 a^{2} - 512 a - 285\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a^{3}-3a^{2}+6a+4\right){x}+205a^{3}+238a^{2}-512a-285$ |
| 8.1-d1 |
8.1-d |
$1$ |
$1$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
8.1 |
\( 2^{3} \) |
\( 2^{12} \) |
$10.06060$ |
$(a^3-5a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 2^{2} \) |
$0.004610597$ |
$825.2501714$ |
0.701234905 |
\( \frac{697025}{16} a^{3} + \frac{64903}{4} a^{2} - \frac{390197}{2} a - \frac{1492455}{16} \) |
\( \bigl[a^{3} - 3 a\) , \( a^{2} - a - 3\) , \( a^{3} - 4 a\) , \( a^{2} - 2 a - 1\) , \( a^{2} - a - 2\bigr] \) |
${y}^2+\left(a^{3}-3a\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(a^{2}-2a-1\right){x}+a^{2}-a-2$ |
| 9.1-a1 |
9.1-a |
$2$ |
$2$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{9} \) |
$10.20982$ |
$(-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$221.7514976$ |
1.277136474 |
\( 26957 a^{3} - 200501 a^{2} + 232783 a + 167412 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a\) , \( a^{2} - 3\) , \( 11 a^{3} - 17 a^{2} - 46 a + 72\) , \( -31 a^{3} + 46 a^{2} + 133 a - 187\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+a{x}^{2}+\left(11a^{3}-17a^{2}-46a+72\right){x}-31a^{3}+46a^{2}+133a-187$ |
| 9.1-a2 |
9.1-a |
$2$ |
$2$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$10.20982$ |
$(-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$221.7514976$ |
1.277136474 |
\( -85122708345 a^{3} + 259383464378 a^{2} - 105388792264 a - 124741955118 \) |
\( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} + a^{2} + 4 a - 4\) , \( a^{2} + a - 3\) , \( 4 a^{3} - 3 a^{2} - 9 a + 6\) , \( a^{3} - 3 a^{2} + 11 a - 2\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-4\right){x}^{2}+\left(4a^{3}-3a^{2}-9a+6\right){x}+a^{3}-3a^{2}+11a-2$ |
| 9.1-b1 |
9.1-b |
$2$ |
$2$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{9} \) |
$10.20982$ |
$(-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$135.5530056$ |
0.780692304 |
\( 26957 a^{3} - 200501 a^{2} + 232783 a + 167412 \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} + 4 a\) , \( a^{3} - 4 a\) , \( -2 a^{2} + a + 6\) , \( -a^{2} + a + 2\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(-2a^{2}+a+6\right){x}-a^{2}+a+2$ |
| 9.1-b2 |
9.1-b |
$2$ |
$2$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{9} \) |
$10.20982$ |
$(-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$135.5530056$ |
0.780692304 |
\( -85122708345 a^{3} + 259383464378 a^{2} - 105388792264 a - 124741955118 \) |
\( \bigl[1\) , \( a^{3} - 4 a - 1\) , \( a^{3} + a^{2} - 3 a - 3\) , \( a^{2} - a - 6\) , \( 18 a^{3} + 6 a^{2} - 82 a - 39\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+a^{2}-3a-3\right){y}={x}^{3}+\left(a^{3}-4a-1\right){x}^{2}+\left(a^{2}-a-6\right){x}+18a^{3}+6a^{2}-82a-39$ |
| 12.1-a1 |
12.1-a |
$2$ |
$2$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3 \) |
$10.58365$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 3 \) |
$0.038056356$ |
$1499.347316$ |
1.971748202 |
\( -\frac{628}{3} a^{3} + \frac{5050}{3} a^{2} + \frac{25697}{3} a + \frac{11399}{3} \) |
\( \bigl[a^{2} + a - 2\) , \( -a^{2} + 4\) , \( 0\) , \( 2 a^{3} - a^{2} - 6 a + 6\) , \( a^{3} - 4 a + 3\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(2a^{3}-a^{2}-6a+6\right){x}+a^{3}-4a+3$ |
| 12.1-a2 |
12.1-a |
$2$ |
$2$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{2} \) |
$10.58365$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.019028178$ |
$1499.347316$ |
1.971748202 |
\( -\frac{564145889}{9} a^{3} - \frac{170994877}{9} a^{2} + \frac{2453750884}{9} a + \frac{1181473132}{9} \) |
\( \bigl[a + 1\) , \( a^{3} - a^{2} - 3 a + 4\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - 2 a^{2} + 6\) , \( -4 a^{3} + 4 a + 3\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{3}-a^{2}-3a+4\right){x}^{2}+\left(a^{3}-2a^{2}+6\right){x}-4a^{3}+4a+3$ |
| 12.1-b1 |
12.1-b |
$2$ |
$2$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( 2^{8} \cdot 3 \) |
$10.58365$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$606.2158399$ |
1.745693645 |
\( -\frac{628}{3} a^{3} + \frac{5050}{3} a^{2} + \frac{25697}{3} a + \frac{11399}{3} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{2} + a - 2\) , \( -2 a^{2} - a + 8\) , \( 2 a^{2} - a - 10\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+4a-3\right){x}^{2}+\left(-2a^{2}-a+8\right){x}+2a^{2}-a-10$ |
| 12.1-b2 |
12.1-b |
$2$ |
$2$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
12.1 |
\( 2^{2} \cdot 3 \) |
\( - 2^{4} \cdot 3^{2} \) |
$10.58365$ |
$(a^3+a^2-3a-1), (-a^3+a^2+4a-3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$303.1079199$ |
1.745693645 |
\( -\frac{564145889}{9} a^{3} - \frac{170994877}{9} a^{2} + \frac{2453750884}{9} a + \frac{1181473132}{9} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 0\) , \( -4 a^{3} + 13 a^{2} + 23 a - 42\) , \( -15 a^{3} + 29 a^{2} + 68 a - 111\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}={x}^{3}+\left(a^{3}+a^{2}-4a-3\right){x}^{2}+\left(-4a^{3}+13a^{2}+23a-42\right){x}-15a^{3}+29a^{2}+68a-111$ |
| 16.1-a1 |
16.1-a |
$2$ |
$7$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{22} \) |
$10.97117$ |
$(a^3+a^2-3a-1), (a^3-5a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.3 |
$49$ |
\( 1 \) |
$1$ |
$3.486958308$ |
1.968083757 |
\( -\frac{86072033716457454374729}{128} a^{3} - \frac{49911268233515996542101}{64} a^{2} + \frac{214767870945936202598631}{128} a + \frac{14944751306024822140599}{16} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 4 a\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -220 a^{3} - 81 a^{2} + 660 a - 205\) , \( -2022 a^{3} - 3701 a^{2} + 4168 a + 6685\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-220a^{3}-81a^{2}+660a-205\right){x}-2022a^{3}-3701a^{2}+4168a+6685$ |
| 16.1-a2 |
16.1-a |
$2$ |
$7$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{10} \) |
$10.97117$ |
$(a^3+a^2-3a-1), (a^3-5a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$7$ |
7B.6.1 |
$1$ |
\( 1 \) |
$1$ |
$170.8609571$ |
1.968083757 |
\( -\frac{12687}{128} a^{3} - \frac{1539}{64} a^{2} + \frac{25897}{128} a - \frac{1257}{128} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} - 4 a\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -a^{2} + 5\) , \( a^{2} - 5\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-a^{2}+5\right){x}+a^{2}-5$ |
| 16.1-b1 |
16.1-b |
$2$ |
$3$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{6} \) |
$10.97117$ |
$(a^3+a^2-3a-1), (a^3-5a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3 \) |
$1$ |
$98.38191160$ |
3.399673843 |
\( -\frac{25493935273}{8} a^{3} + \frac{18999224527}{4} a^{2} + \frac{108735799899}{8} a - \frac{155374649783}{8} \) |
\( \bigl[a^{2} - 2\) , \( a + 1\) , \( a^{2} + a - 2\) , \( a^{3} - 3 a^{2} + 5 a - 6\) , \( 2 a^{3} - 10 a^{2} + 13 a - 4\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a^{3}-3a^{2}+5a-6\right){x}+2a^{3}-10a^{2}+13a-4$ |
| 16.1-b2 |
16.1-b |
$2$ |
$3$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{18} \) |
$10.97117$ |
$(a^3+a^2-3a-1), (a^3-5a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 3^{3} \) |
$1$ |
$10.93132351$ |
3.399673843 |
\( \frac{321808737154811547}{512} a^{3} - \frac{487231409593550209}{256} a^{2} + \frac{388178887872068995}{512} a + \frac{465063410326377085}{512} \) |
\( \bigl[a^{2} - 2\) , \( a + 1\) , \( a^{2} + a - 2\) , \( 201 a^{3} - 383 a^{2} - 130 a + 44\) , \( 2428 a^{3} - 8859 a^{2} + 5447 a + 5098\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(201a^{3}-383a^{2}-130a+44\right){x}+2428a^{3}-8859a^{2}+5447a+5098$ |
| 16.1-c1 |
16.1-c |
$2$ |
$2$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{11} \) |
$10.97117$ |
$(a^3+a^2-3a-1), (a^3-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$93.72958593$ |
0.539818103 |
\( \frac{1597366350419001}{32} a^{3} - \frac{1191570141116195}{16} a^{2} - \frac{6814521133690839}{32} a + \frac{9741653871127927}{32} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - 4 a\) , \( 22 a^{3} - 50 a^{2} - a + 15\) , \( -131 a^{3} + 370 a^{2} - 124 a - 167\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-2\right){x}^{2}+\left(22a^{3}-50a^{2}-a+15\right){x}-131a^{3}+370a^{2}-124a-167$ |
| 16.1-c2 |
16.1-c |
$2$ |
$2$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( - 2^{13} \) |
$10.97117$ |
$(a^3+a^2-3a-1), (a^3-5a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$93.72958593$ |
0.539818103 |
\( -\frac{96738191432249}{1024} a^{3} - \frac{18314133599365}{512} a^{2} + \frac{432983750977167}{1024} a + \frac{210320680302833}{1024} \) |
\( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 4\) , \( a\) , \( -109 a^{3} - 121 a^{2} + 270 a + 123\) , \( -1530 a^{3} - 1719 a^{2} + 3860 a + 1981\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+a{y}={x}^{3}+\left(-a^{2}+a+4\right){x}^{2}+\left(-109a^{3}-121a^{2}+270a+123\right){x}-1530a^{3}-1719a^{2}+3860a+1981$ |
| 16.1-d1 |
16.1-d |
$2$ |
$5$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{4} \) |
$10.97117$ |
$(a^3+a^2-3a-1), (a^3-5a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.2 |
$25$ |
\( 1 \) |
$1$ |
$3.861379645$ |
1.111944866 |
\( -\frac{370030855770024440062489}{2} a^{3} + \frac{552055851676808784700003}{2} a^{2} + 789293916809435415312474 a - \frac{2256659864632090143523525}{2} \) |
\( \bigl[a^{3} - 4 a\) , \( -a^{3} - a^{2} + 3 a + 4\) , \( 0\) , \( -3996 a^{3} - 1679 a^{2} + 17533 a + 8558\) , \( 6065 a^{3} + 71 a^{2} - 32559 a - 15311\bigr] \) |
${y}^2+\left(a^{3}-4a\right){x}{y}={x}^{3}+\left(-a^{3}-a^{2}+3a+4\right){x}^{2}+\left(-3996a^{3}-1679a^{2}+17533a+8558\right){x}+6065a^{3}+71a^{2}-32559a-15311$ |
| 16.1-d2 |
16.1-d |
$2$ |
$5$ |
4.4.7537.1 |
$4$ |
$[4, 0]$ |
16.1 |
\( 2^{4} \) |
\( 2^{20} \) |
$10.97117$ |
$(a^3+a^2-3a-1), (a^3-5a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$5$ |
5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$96.53449113$ |
1.111944866 |
\( \frac{58869129}{32} a^{3} + \frac{22852913}{32} a^{2} - \frac{263593245}{32} a - \frac{65166623}{16} \) |
\( \bigl[a\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -14 a^{3} + 22 a^{2} + 61 a - 88\) , \( 71 a^{3} - 106 a^{2} - 303 a + 432\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-3a-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(-14a^{3}+22a^{2}+61a-88\right){x}+71a^{3}-106a^{2}-303a+432$ |
*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.
