| 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 |
$2$ |
$3$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.57801$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$1$ |
$116.2880813$ |
0.982357678 |
\( -39346931 a^{3} - 47559540 a^{2} + 131053770 a + 53434185 \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} + a - 4\) , \( a^{3} - 5 a + 1\) , \( -9 a^{3} + 46 a^{2} - 38 a - 15\) , \( -3 a^{3} + 30 a^{2} - 29 a - 18\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(-9a^{3}+46a^{2}-38a-15\right){x}-3a^{3}+30a^{2}-29a-18$ |
| 1.1-a2 |
1.1-a |
$2$ |
$3$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.57801$ |
$\textsf{none}$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B.1.1 |
$1$ |
\( 1 \) |
$1$ |
$1046.592732$ |
0.982357678 |
\( -211822760 a^{3} + 290798826 a^{2} + 1162516086 a - 1704375723 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 1\) , \( a - 1\) , \( 1\) , \( -a^{2} + 3 a + 1\) , \( -a^{3} + a^{2} + a\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a^{2}+3a+1\right){x}-a^{3}+a^{2}+a$ |
| 1.1-b1 |
1.1-b |
$2$ |
$3$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.57801$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$199.7789155$ |
1.687656631 |
\( -39346931 a^{3} - 47559540 a^{2} + 131053770 a + 53434185 \) |
\( \bigl[a^{2} - 2\) , \( -a^{3} + 6 a - 1\) , \( a + 1\) , \( 2 a^{3} + 2 a^{2} - 13 a - 3\) , \( -a^{3} + 4 a + 1\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+6a-1\right){x}^{2}+\left(2a^{3}+2a^{2}-13a-3\right){x}-a^{3}+4a+1$ |
| 1.1-b2 |
1.1-b |
$2$ |
$3$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
1.1 |
\( 1 \) |
\( 1 \) |
$10.57801$ |
$\textsf{none}$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
✓ |
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$199.7789155$ |
1.687656631 |
\( -211822760 a^{3} + 290798826 a^{2} + 1162516086 a - 1704375723 \) |
\( \bigl[a^{3} - 5 a + 2\) , \( -a^{2} + 2\) , \( 1\) , \( -a^{2} - a + 7\) , \( -a^{2} + 4\bigr] \) |
${y}^2+\left(a^{3}-5a+2\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-a^{2}-a+7\right){x}-a^{2}+4$ |
| 3.2-a1 |
3.2-a |
$2$ |
$2$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{20} \) |
$12.13513$ |
$(-a^3-a^2+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$106.8237727$ |
1.804813566 |
\( \frac{34044032225374258}{3486784401} a^{3} - \frac{15568732228609135}{1162261467} a^{2} - \frac{20756828103424502}{387420489} a + \frac{91272766085090498}{1162261467} \) |
\( \bigl[a^{3} - 5 a + 2\) , \( a^{2} - a - 2\) , \( 0\) , \( -4 a^{3} + 12 a^{2} - 4 a - 8\) , \( -22 a^{3} + 71 a^{2} - 35 a - 34\bigr] \) |
${y}^2+\left(a^{3}-5a+2\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-4a^{3}+12a^{2}-4a-8\right){x}-22a^{3}+71a^{2}-35a-34$ |
| 3.2-a2 |
3.2-a |
$2$ |
$2$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{10} \) |
$12.13513$ |
$(-a^3-a^2+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$427.2950911$ |
1.804813566 |
\( -\frac{55718947}{59049} a^{3} + \frac{37572550}{19683} a^{2} + \frac{33738866}{6561} a - \frac{147185429}{19683} \) |
\( \bigl[a^{3} - 5 a + 2\) , \( a^{2} - a - 2\) , \( 0\) , \( a^{3} - 3 a^{2} + a + 2\) , \( 0\bigr] \) |
${y}^2+\left(a^{3}-5a+2\right){x}{y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(a^{3}-3a^{2}+a+2\right){x}$ |
| 3.2-b1 |
3.2-b |
$2$ |
$2$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( - 3^{20} \) |
$12.13513$ |
$(-a^3-a^2+4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 5 \) |
$0.035893362$ |
$283.5857958$ |
1.719741039 |
\( \frac{34044032225374258}{3486784401} a^{3} - \frac{15568732228609135}{1162261467} a^{2} - \frac{20756828103424502}{387420489} a + \frac{91272766085090498}{1162261467} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + 4 a\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -2 a^{3} + 4 a^{2} + 8 a - 23\) , \( 9 a^{3} - 7 a^{2} - 51 a + 45\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(-2a^{3}+4a^{2}+8a-23\right){x}+9a^{3}-7a^{2}-51a+45$ |
| 3.2-b2 |
3.2-b |
$2$ |
$2$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
3.2 |
\( 3 \) |
\( 3^{10} \) |
$12.13513$ |
$(-a^3-a^2+4a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.017946681$ |
$1134.343183$ |
1.719741039 |
\( -\frac{55718947}{59049} a^{3} + \frac{37572550}{19683} a^{2} + \frac{33738866}{6561} a - \frac{147185429}{19683} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} + 4 a\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -2 a^{3} - a^{2} + 8 a + 2\) , \( -a^{3} - a^{2} + 4 a + 3\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}+4a\right){x}^{2}+\left(-2a^{3}-a^{2}+8a+2\right){x}-a^{3}-a^{2}+4a+3$ |
| 7.1-a1 |
7.1-a |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{4} \) |
$13.49091$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.127589165$ |
$90.98097038$ |
3.466537393 |
\( -\frac{78532003504198177}{2401} a^{3} + \frac{264784293303148002}{2401} a^{2} - \frac{156789935149360725}{2401} a - \frac{99337444570620006}{2401} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -a^{3} + 4 a - 1\) , \( a + 1\) , \( 5 a^{3} - 11 a^{2} + a - 2\) , \( 21 a^{3} - 72 a^{2} + 42 a + 35\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+4a-1\right){x}^{2}+\left(5a^{3}-11a^{2}+a-2\right){x}+21a^{3}-72a^{2}+42a+35$ |
| 7.1-a2 |
7.1-a |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$13.49091$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.563794582$ |
$363.9238815$ |
3.466537393 |
\( -\frac{33315631}{49} a^{3} + \frac{174318870}{49} a^{2} - \frac{138669633}{49} a - \frac{77634015}{49} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( -a^{3} + 4 a - 1\) , \( a + 1\) , \( -a^{2} + a + 3\) , \( a^{3} - a^{2} - a - 1\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{3}+4a-1\right){x}^{2}+\left(-a^{2}+a+3\right){x}+a^{3}-a^{2}-a-1$ |
| 7.1-a3 |
7.1-a |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{6} \) |
$13.49091$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \cdot 3 \) |
$0.187931527$ |
$363.9238815$ |
3.466537393 |
\( \frac{42491675}{117649} a^{3} + \frac{105473406}{117649} a^{2} - \frac{149022567}{117649} a - \frac{155580594}{117649} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( a^{3} - 4 a + 2\) , \( a^{2} - 2\) , \( a^{3} - a^{2} - 3 a + 5\) , \( -2 a^{3} + 3 a^{2} + 10 a - 15\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-4a+2\right){x}^{2}+\left(a^{3}-a^{2}-3a+5\right){x}-2a^{3}+3a^{2}+10a-15$ |
| 7.1-a4 |
7.1-a |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{12} \) |
$13.49091$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.375863055$ |
$90.98097038$ |
3.466537393 |
\( \frac{2510916576253787}{13841287201} a^{3} - \frac{3414275543286024}{13841287201} a^{2} - \frac{14093718613862301}{13841287201} a + \frac{20744241156004575}{13841287201} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 6 a - 1\) , \( a^{3} - 5 a + 1\) , \( 31 a^{3} + 41 a^{2} - 105 a - 48\) , \( 290 a^{3} + 354 a^{2} - 968 a - 403\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-1\right){x}^{2}+\left(31a^{3}+41a^{2}-105a-48\right){x}+290a^{3}+354a^{2}-968a-403$ |
| 7.1-b1 |
7.1-b |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{6} \) |
$13.49091$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.266976428$ |
$1212.089814$ |
1.822430187 |
\( \frac{42491675}{117649} a^{3} + \frac{105473406}{117649} a^{2} - \frac{149022567}{117649} a - \frac{155580594}{117649} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} - 4 a\) , \( a^{2} - 2\) , \( -3 a^{3} + 3 a^{2} + 17 a - 20\) , \( 7 a^{3} - 10 a^{2} - 38 a + 56\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(a^{3}-4a\right){x}^{2}+\left(-3a^{3}+3a^{2}+17a-20\right){x}+7a^{3}-10a^{2}-38a+56$ |
| 7.1-b2 |
7.1-b |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{4} \) |
$13.49091$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$1.601858570$ |
$33.66916151$ |
1.822430187 |
\( -\frac{78532003504198177}{2401} a^{3} + \frac{264784293303148002}{2401} a^{2} - \frac{156789935149360725}{2401} a - \frac{99337444570620006}{2401} \) |
\( \bigl[1\) , \( a^{2} - 4\) , \( a^{3} + a^{2} - 5 a - 2\) , \( 68 a^{3} + 40 a^{2} - 351 a - 153\) , \( 477 a^{3} + 257 a^{2} - 2468 a - 940\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+a^{2}-5a-2\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(68a^{3}+40a^{2}-351a-153\right){x}+477a^{3}+257a^{2}-2468a-940$ |
| 7.1-b3 |
7.1-b |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( 7^{2} \) |
$13.49091$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$0.800929285$ |
$134.6766460$ |
1.822430187 |
\( -\frac{33315631}{49} a^{3} + \frac{174318870}{49} a^{2} - \frac{138669633}{49} a - \frac{77634015}{49} \) |
\( \bigl[1\) , \( a^{2} - 4\) , \( a^{3} + a^{2} - 5 a - 2\) , \( 3 a^{3} - 16 a + 2\) , \( 12 a^{3} + 8 a^{2} - 62 a - 33\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+a^{2}-5a-2\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(3a^{3}-16a+2\right){x}+12a^{3}+8a^{2}-62a-33$ |
| 7.1-b4 |
7.1-b |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.1 |
\( 7 \) |
\( - 7^{12} \) |
$13.49091$ |
$(a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.533952856$ |
$303.0224536$ |
1.822430187 |
\( \frac{2510916576253787}{13841287201} a^{3} - \frac{3414275543286024}{13841287201} a^{2} - \frac{14093718613862301}{13841287201} a + \frac{20744241156004575}{13841287201} \) |
\( \bigl[1\) , \( -a^{3} + 5 a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 87 a^{3} + 104 a^{2} - 287 a - 116\) , \( 1159 a^{3} + 1398 a^{2} - 3860 a - 1573\bigr] \) |
${y}^2+{x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{3}+5a-1\right){x}^{2}+\left(87a^{3}+104a^{2}-287a-116\right){x}+1159a^{3}+1398a^{2}-3860a-1573$ |
| 7.2-a1 |
7.2-a |
$1$ |
$1$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{5} \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$320.0004269$ |
2.703242438 |
\( \frac{33271808}{16807} a^{3} - \frac{136597504}{16807} a^{2} + \frac{15806464}{2401} a + \frac{70148096}{16807} \) |
\( \bigl[0\) , \( -a^{3} + 6 a - 1\) , \( a^{2} + a - 2\) , \( 22 a^{3} + 11 a^{2} - 114 a - 38\) , \( -13 a^{3} - 7 a^{2} + 66 a + 22\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{3}+6a-1\right){x}^{2}+\left(22a^{3}+11a^{2}-114a-38\right){x}-13a^{3}-7a^{2}+66a+22$ |
| 7.2-b1 |
7.2-b |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7^{6} \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$454.7235086$ |
1.920666009 |
\( \frac{49173444992333}{117649} a^{3} - \frac{67503561347319}{117649} a^{2} - \frac{38555793505035}{16807} a + \frac{395685288167970}{117649} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 4\) , \( a^{2} + a - 3\) , \( -6 a^{3} + 6 a^{2} + 34 a - 44\) , \( -12 a^{3} + 16 a^{2} + 64 a - 93\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-6a^{3}+6a^{2}+34a-44\right){x}-12a^{3}+16a^{2}+64a-93$ |
| 7.2-b2 |
7.2-b |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{3} \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$909.4470172$ |
1.920666009 |
\( \frac{2317970}{343} a^{3} - \frac{3048576}{343} a^{2} - \frac{1797021}{49} a + \frac{18118740}{343} \) |
\( \bigl[a^{2} + a - 2\) , \( a^{2} - a - 4\) , \( a^{2} + a - 3\) , \( -a^{3} + a^{2} + 4 a - 4\) , \( a^{2} - 3\bigr] \) |
${y}^2+\left(a^{2}+a-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-4\right){x}^{2}+\left(-a^{3}+a^{2}+4a-4\right){x}+a^{2}-3$ |
| 7.2-b3 |
7.2-b |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7^{2} \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1$ |
$454.7235086$ |
1.920666009 |
\( -\frac{246599163837484}{49} a^{3} - \frac{132306143675838}{49} a^{2} + \frac{182329081724214}{7} a + \frac{481475007197355}{49} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + a^{2} + 5 a - 4\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 21 a^{3} + 10 a^{2} - 113 a - 37\) , \( -72 a^{3} - 40 a^{2} + 367 a + 137\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-4\right){x}^{2}+\left(21a^{3}+10a^{2}-113a-37\right){x}-72a^{3}-40a^{2}+367a+137$ |
| 7.2-b4 |
7.2-b |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( -7 \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1$ |
$909.4470172$ |
1.920666009 |
\( \frac{7043852}{7} a^{3} + \frac{3716616}{7} a^{2} - 5210172 a - \frac{13434117}{7} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + a^{2} + 5 a - 4\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} - 8 a + 3\) , \( -a^{3} + 3 a - 1\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-4\right){x}^{2}+\left(a^{3}-8a+3\right){x}-a^{3}+3a-1$ |
| 7.2-c1 |
7.2-c |
$2$ |
$3$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{3} \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
$0 \le r \le 1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.2 |
|
\( 3 \) |
$1$ |
$13.90362581$ |
3.158699648 |
\( -\frac{1217501548544}{343} a^{3} + \frac{1334880890880}{343} a^{2} + \frac{914391613440}{49} a - \frac{8569824079872}{343} \) |
\( \bigl[0\) , \( a^{2} - 3\) , \( a^{2} + a - 3\) , \( 3 a^{3} - 11 a^{2} + 7 a + 4\) , \( 35 a^{3} - 123 a^{2} + 77 a + 45\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(3a^{3}-11a^{2}+7a+4\right){x}+35a^{3}-123a^{2}+77a+45$ |
| 7.2-c2 |
7.2-c |
$2$ |
$3$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{9} \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
$0 \le r \le 1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B.1.1 |
|
\( 3^{2} \) |
$1$ |
$125.1326323$ |
3.158699648 |
\( -\frac{1137913341833216}{40353607} a^{3} - \frac{610499221524480}{40353607} a^{2} + \frac{841342778007552}{5764801} a + \frac{2221625535885312}{40353607} \) |
\( \bigl[0\) , \( -a^{3} + 5 a\) , \( a^{3} - 4 a + 1\) , \( -18 a^{3} + 56 a^{2} - 27 a - 20\) , \( -353 a^{3} + 1187 a^{2} - 699 a - 446\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(-18a^{3}+56a^{2}-27a-20\right){x}-353a^{3}+1187a^{2}-699a-446$ |
| 7.2-d1 |
7.2-d |
$2$ |
$3$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{3} \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$107.4170602$ |
0.907418650 |
\( -\frac{1217501548544}{343} a^{3} + \frac{1334880890880}{343} a^{2} + \frac{914391613440}{49} a - \frac{8569824079872}{343} \) |
\( \bigl[0\) , \( -a^{2} + 3\) , \( a^{3} - 4 a + 1\) , \( 2 a^{3} + 3 a^{2} - 10 a - 14\) , \( a^{3} - a^{2} - 5 a + 3\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(2a^{3}+3a^{2}-10a-14\right){x}+a^{3}-a^{2}-5a+3$ |
| 7.2-d2 |
7.2-d |
$2$ |
$3$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{9} \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$3$ |
3B |
$1$ |
\( 1 \) |
$1$ |
$107.4170602$ |
0.907418650 |
\( -\frac{1137913341833216}{40353607} a^{3} - \frac{610499221524480}{40353607} a^{2} + \frac{841342778007552}{5764801} a + \frac{2221625535885312}{40353607} \) |
\( \bigl[0\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( a\) , \( -a^{3} + 3 a^{2} + 4 a - 8\) , \( 2 a^{2} - 9 a + 7\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a^{3}-a^{2}+4a+3\right){x}^{2}+\left(-a^{3}+3a^{2}+4a-8\right){x}+2a^{2}-9a+7$ |
| 7.2-e1 |
7.2-e |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7^{6} \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$0.371311704$ |
$978.6788820$ |
2.046548475 |
\( \frac{49173444992333}{117649} a^{3} - \frac{67503561347319}{117649} a^{2} - \frac{38555793505035}{16807} a + \frac{395685288167970}{117649} \) |
\( \bigl[a^{2} - 3\) , \( a^{2} - a - 3\) , \( a^{3} + a^{2} - 4 a - 1\) , \( 20 a^{3} - 78 a^{2} + 59 a + 22\) , \( -207 a^{3} + 699 a^{2} - 425 a - 247\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(20a^{3}-78a^{2}+59a+22\right){x}-207a^{3}+699a^{2}-425a-247$ |
| 7.2-e2 |
7.2-e |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{3} \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$0.742623408$ |
$978.6788820$ |
2.046548475 |
\( \frac{2317970}{343} a^{3} - \frac{3048576}{343} a^{2} - \frac{1797021}{49} a + \frac{18118740}{343} \) |
\( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{2} + a - 3\) , \( 5 a^{2} + 3 a - 16\) , \( 3 a^{3} + a^{2} - 13 a + 6\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(5a^{2}+3a-16\right){x}+3a^{3}+a^{2}-13a+6$ |
| 7.2-e3 |
7.2-e |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( -7 \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$2.227870225$ |
$108.7420980$ |
2.046548475 |
\( \frac{7043852}{7} a^{3} + \frac{3716616}{7} a^{2} - 5210172 a - \frac{13434117}{7} \) |
\( \bigl[1\) , \( a^{2} - 4\) , \( 1\) , \( -2 a + 3\) , \( -a^{2} + 2 a - 1\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-2a+3\right){x}-a^{2}+2a-1$ |
| 7.2-e4 |
7.2-e |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( 7^{2} \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1.113935112$ |
$108.7420980$ |
2.046548475 |
\( -\frac{246599163837484}{49} a^{3} - \frac{132306143675838}{49} a^{2} + \frac{182329081724214}{7} a + \frac{481475007197355}{49} \) |
\( \bigl[1\) , \( a^{2} - 4\) , \( 1\) , \( -10 a^{2} + 8 a + 8\) , \( -29 a^{2} + 34 a + 15\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-10a^{2}+8a+8\right){x}-29a^{2}+34a+15$ |
| 7.2-f1 |
7.2-f |
$1$ |
$1$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
7.2 |
\( 7 \) |
\( - 7^{5} \) |
$13.49091$ |
$(2a^3+2a^2-7a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 5 \) |
$0.039696125$ |
$209.2531531$ |
1.403409995 |
\( \frac{33271808}{16807} a^{3} - \frac{136597504}{16807} a^{2} + \frac{15806464}{2401} a + \frac{70148096}{16807} \) |
\( \bigl[0\) , \( a^{3} - a^{2} - 5 a + 4\) , \( a\) , \( 2 a^{3} - 3 a^{2} - 7 a + 9\) , \( a^{3} - 3 a^{2} - 2 a + 7\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a^{3}-a^{2}-5a+4\right){x}^{2}+\left(2a^{3}-3a^{2}-7a+9\right){x}+a^{3}-3a^{2}-2a+7$ |
| 9.1-a1 |
9.1-a |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$13.92145$ |
$(-a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$2.787732478$ |
$19.36205956$ |
1.823883426 |
\( 1143580865460373946558 a^{3} + 1381441051814657392038 a^{2} - 3811268947799766073014 a - 1553781201145096895583 \) |
\( \bigl[a^{2} + a - 3\) , \( 0\) , \( a^{2} + a - 3\) , \( 3392 a^{3} + 1820 a^{2} - 17556 a - 6627\) , \( -6102 a^{3} - 3274 a^{2} + 31581 a + 11911\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(3392a^{3}+1820a^{2}-17556a-6627\right){x}-6102a^{3}-3274a^{2}+31581a+11911$ |
| 9.1-a2 |
9.1-a |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$13.92145$ |
$(-a^3+5a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.464622079$ |
$2091.102432$ |
1.823883426 |
\( -4120 a^{3} + 12405 a^{2} + 24480 a - 64824 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{3} + a^{2} - 5 a - 1\) , \( 3 a^{3} + 3 a^{2} - 11 a - 5\) , \( 2 a^{3} + 2 a^{2} - 7 a - 3\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-1\right){x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(3a^{3}+3a^{2}-11a-5\right){x}+2a^{3}+2a^{2}-7a-3$ |
| 9.1-a3 |
9.1-a |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$13.92145$ |
$(-a^3+5a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.929244159$ |
$522.7756081$ |
1.823883426 |
\( 503119874 a^{3} - 754384902 a^{2} - 2767060989 a + 4392485634 \) |
\( \bigl[a^{3} + a^{2} - 5 a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a^{3} + a^{2} - 5 a - 1\) , \( -2 a^{3} - 2 a^{2} + 4 a - 5\) , \( -32 a^{3} - 39 a^{2} + 107 a + 48\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-1\right){x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(a^{3}+a^{2}-4a-1\right){x}^{2}+\left(-2a^{3}-2a^{2}+4a-5\right){x}-32a^{3}-39a^{2}+107a+48$ |
| 9.1-a4 |
9.1-a |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$13.92145$ |
$(-a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2 \) |
$1.393866239$ |
$77.44823824$ |
1.823883426 |
\( 12002689028 a^{3} + 14504638908 a^{2} - 40008289104 a - 16311146127 \) |
\( \bigl[a^{3} - 5 a + 1\) , \( a^{3} - 5 a + 2\) , \( a^{3} - 4 a + 2\) , \( 7 a^{3} - 13 a^{2} - 41 a + 68\) , \( 31 a^{3} - 50 a^{2} - 176 a + 276\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(a^{3}-4a+2\right){y}={x}^{3}+\left(a^{3}-5a+2\right){x}^{2}+\left(7a^{3}-13a^{2}-41a+68\right){x}+31a^{3}-50a^{2}-176a+276$ |
| 9.1-b1 |
9.1-b |
$2$ |
$2$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$13.92145$ |
$(-a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.848346264$ |
$47.79782066$ |
2.985285419 |
\( -\frac{5146378536747278}{27} a^{3} - \frac{2761151903498969}{27} a^{2} + \frac{26635697035413319}{27} a + \frac{1116455267731694}{3} \) |
\( \bigl[a^{3} - 5 a + 2\) , \( -a^{3} + a^{2} + 6 a - 4\) , \( a^{2} + a - 3\) , \( a^{3} + 3 a^{2} - 9 a - 3\) , \( -7 a^{3} + 57 a^{2} - 74 a - 40\bigr] \) |
${y}^2+\left(a^{3}-5a+2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-4\right){x}^{2}+\left(a^{3}+3a^{2}-9a-3\right){x}-7a^{3}+57a^{2}-74a-40$ |
| 9.1-b2 |
9.1-b |
$2$ |
$2$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$13.92145$ |
$(-a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.924173132$ |
$191.1912826$ |
2.985285419 |
\( \frac{55506679}{9} a^{3} + \frac{29810663}{9} a^{2} - \frac{95773390}{3} a - 12043491 \) |
\( \bigl[a^{3} - 5 a + 2\) , \( -a^{3} + a^{2} + 6 a - 4\) , \( a^{2} + a - 3\) , \( a^{3} - 7 a^{2} + 6 a + 12\) , \( -5 a^{3} + 13 a^{2} - 2 a - 7\bigr] \) |
${y}^2+\left(a^{3}-5a+2\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-4\right){x}^{2}+\left(a^{3}-7a^{2}+6a+12\right){x}-5a^{3}+13a^{2}-2a-7$ |
| 9.1-c1 |
9.1-c |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$13.92145$ |
$(-a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$1.970891894$ |
$48.42451703$ |
3.224946629 |
\( 503119874 a^{3} - 754384902 a^{2} - 2767060989 a + 4392485634 \) |
\( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 6 a - 1\) , \( a^{3} - 4 a + 2\) , \( -22 a^{3} - 8 a^{2} + 53 a + 23\) , \( -109 a^{3} - 67 a^{2} + 289 a + 107\bigr] \) |
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{3}-4a+2\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-1\right){x}^{2}+\left(-22a^{3}-8a^{2}+53a+23\right){x}-109a^{3}-67a^{2}+289a+107$ |
| 9.1-c2 |
9.1-c |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$13.92145$ |
$(-a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$2.956337842$ |
$64.56602271$ |
3.224946629 |
\( 12002689028 a^{3} + 14504638908 a^{2} - 40008289104 a - 16311146127 \) |
\( \bigl[a\) , \( a^{2} - 3\) , \( a^{3} + a^{2} - 5 a - 1\) , \( -a^{3} - 11 a^{2} + 5 a + 24\) , \( -10 a^{3} - 25 a^{2} + 68 a - 11\bigr] \) |
${y}^2+a{x}{y}+\left(a^{3}+a^{2}-5a-1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{3}-11a^{2}+5a+24\right){x}-10a^{3}-25a^{2}+68a-11$ |
| 9.1-c3 |
9.1-c |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{6} \) |
$13.92145$ |
$(-a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.985445947$ |
$193.6980681$ |
3.224946629 |
\( -4120 a^{3} + 12405 a^{2} + 24480 a - 64824 \) |
\( \bigl[a^{3} - 5 a + 2\) , \( a^{3} - a^{2} - 4 a + 5\) , \( a^{3} - 5 a + 1\) , \( 6 a^{3} - a^{2} - 33 a + 14\) , \( 9 a^{3} - a^{2} - 47 a + 11\bigr] \) |
${y}^2+\left(a^{3}-5a+2\right){x}{y}+\left(a^{3}-5a+1\right){y}={x}^{3}+\left(a^{3}-a^{2}-4a+5\right){x}^{2}+\left(6a^{3}-a^{2}-33a+14\right){x}+9a^{3}-a^{2}-47a+11$ |
| 9.1-c4 |
9.1-c |
$4$ |
$6$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( - 3^{6} \) |
$13.92145$ |
$(-a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
✓ |
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$5.912675684$ |
$16.14150567$ |
3.224946629 |
\( 1143580865460373946558 a^{3} + 1381441051814657392038 a^{2} - 3811268947799766073014 a - 1553781201145096895583 \) |
\( \bigl[a^{3} - 4 a + 2\) , \( a^{2} + a - 4\) , \( a^{3} - 5 a + 2\) , \( 109 a^{3} + 45 a^{2} - 534 a - 206\) , \( 53 a^{3} - 52 a^{2} - 127 a - 41\bigr] \) |
${y}^2+\left(a^{3}-4a+2\right){x}{y}+\left(a^{3}-5a+2\right){y}={x}^{3}+\left(a^{2}+a-4\right){x}^{2}+\left(109a^{3}+45a^{2}-534a-206\right){x}+53a^{3}-52a^{2}-127a-41$ |
| 9.1-d1 |
9.1-d |
$2$ |
$2$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{14} \) |
$13.92145$ |
$(-a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.185835847$ |
$375.6660225$ |
2.358988592 |
\( -\frac{5146378536747278}{27} a^{3} - \frac{2761151903498969}{27} a^{2} + \frac{26635697035413319}{27} a + \frac{1116455267731694}{3} \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( 95 a^{3} + 58 a^{2} - 494 a - 218\) , \( -775 a^{3} - 425 a^{2} + 4011 a + 1557\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(95a^{3}+58a^{2}-494a-218\right){x}-775a^{3}-425a^{2}+4011a+1557$ |
| 9.1-d2 |
9.1-d |
$2$ |
$2$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.1 |
\( 3^{2} \) |
\( 3^{10} \) |
$13.92145$ |
$(-a^3+5a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.092917923$ |
$1502.664090$ |
2.358988592 |
\( \frac{55506679}{9} a^{3} + \frac{29810663}{9} a^{2} - \frac{95773390}{3} a - 12043491 \) |
\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{2} + a + 2\) , \( a^{2} + a - 2\) , \( 5 a^{3} + 3 a^{2} - 29 a - 8\) , \( -8 a^{3} - 6 a^{2} + 42 a + 21\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-4a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(5a^{3}+3a^{2}-29a-8\right){x}-8a^{3}-6a^{2}+42a+21$ |
| 9.2-a1 |
9.2-a |
$4$ |
$4$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$13.92145$ |
$(-a^3+5a), (-a^3-a^2+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$488.3710490$ |
3.094180274 |
\( \frac{8033730533}{3} a^{3} + \frac{29802495703}{9} a^{2} - \frac{81124261510}{9} a - \frac{33140563763}{9} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} + a^{2} - 6 a - 2\) , \( a^{3} - 4 a + 1\) , \( 687 a^{3} + 367 a^{2} - 3560 a - 1336\) , \( -12585 a^{3} - 6752 a^{2} + 65135 a + 24571\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-2\right){x}^{2}+\left(687a^{3}+367a^{2}-3560a-1336\right){x}-12585a^{3}-6752a^{2}+65135a+24571$ |
| 9.2-a2 |
9.2-a |
$4$ |
$4$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{4} \) |
$13.92145$ |
$(-a^3+5a), (-a^3-a^2+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$488.3710490$ |
3.094180274 |
\( -\frac{56596}{3} a^{3} - 30615 a^{2} + \frac{203077}{3} a + \frac{172117}{3} \) |
\( \bigl[a^{2} + a - 3\) , \( a^{3} + a^{2} - 6 a - 2\) , \( a^{3} - 4 a + 1\) , \( 247 a^{3} + 132 a^{2} - 1280 a - 476\) , \( 2812 a^{3} + 1509 a^{2} - 14554 a - 5491\bigr] \) |
${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-2\right){x}^{2}+\left(247a^{3}+132a^{2}-1280a-476\right){x}+2812a^{3}+1509a^{2}-14554a-5491$ |
| 9.2-a3 |
9.2-a |
$4$ |
$4$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{4} \) |
$13.92145$ |
$(-a^3+5a), (-a^3-a^2+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 3 \) |
$1$ |
$488.3710490$ |
3.094180274 |
\( \frac{172877042666873288704}{3} a^{3} + 69611589021061548285 a^{2} - \frac{576155936500787187703}{3} a - \frac{234887717273225527576}{3} \) |
\( \bigl[a^{3} + a^{2} - 5 a - 2\) , \( 0\) , \( a^{3} - 4 a + 1\) , \( 471 a^{3} + 240 a^{2} - 2401 a - 942\) , \( -8218 a^{3} - 4536 a^{2} + 42731 a + 16225\bigr] \) |
${y}^2+\left(a^{3}+a^{2}-5a-2\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(471a^{3}+240a^{2}-2401a-942\right){x}-8218a^{3}-4536a^{2}+42731a+16225$ |
| 9.2-a4 |
9.2-a |
$4$ |
$4$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{16} \) |
$13.92145$ |
$(-a^3+5a), (-a^3-a^2+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$30.52319056$ |
3.094180274 |
\( -\frac{808246253471217664}{81} a^{3} + \frac{302793629992226587}{9} a^{2} - \frac{1613671792723620083}{81} a - \frac{1022374501792619432}{81} \) |
\( \bigl[a^{3} - 5 a + 1\) , \( -a^{3} + 5 a\) , \( a^{3} + a^{2} - 4 a - 1\) , \( -143 a^{3} - 191 a^{2} + 465 a + 268\) , \( 1940 a^{3} + 2281 a^{2} - 6514 a - 2402\bigr] \) |
${y}^2+\left(a^{3}-5a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-1\right){y}={x}^{3}+\left(-a^{3}+5a\right){x}^{2}+\left(-143a^{3}-191a^{2}+465a+268\right){x}+1940a^{3}+2281a^{2}-6514a-2402$ |
| 9.2-b1 |
9.2-b |
$4$ |
$4$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{16} \) |
$13.92145$ |
$(-a^3+5a), (-a^3-a^2+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$19.60048161$ |
0.662309787 |
\( -\frac{808246253471217664}{81} a^{3} + \frac{302793629992226587}{9} a^{2} - \frac{1613671792723620083}{81} a - \frac{1022374501792619432}{81} \) |
\( \bigl[a^{2} - 3\) , \( a^{3} + a^{2} - 6 a - 1\) , \( a^{2} + a - 2\) , \( -29 a^{3} - 112 a^{2} + 38 a + 349\) , \( 230 a^{3} + 707 a^{2} - 444 a - 1948\bigr] \) |
${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a^{3}+a^{2}-6a-1\right){x}^{2}+\left(-29a^{3}-112a^{2}+38a+349\right){x}+230a^{3}+707a^{2}-444a-1948$ |
| 9.2-b2 |
9.2-b |
$4$ |
$4$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{4} \) |
$13.92145$ |
$(-a^3+5a), (-a^3-a^2+4a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$78.40192646$ |
0.662309787 |
\( \frac{172877042666873288704}{3} a^{3} + 69611589021061548285 a^{2} - \frac{576155936500787187703}{3} a - \frac{234887717273225527576}{3} \) |
\( \bigl[a^{3} - 4 a + 1\) , \( a^{2} - a - 2\) , \( a^{2} + a - 3\) , \( 265 a^{3} - 841 a^{2} + 433 a + 287\) , \( 9624 a^{3} - 32279 a^{2} + 18906 a + 12022\bigr] \) |
${y}^2+\left(a^{3}-4a+1\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(265a^{3}-841a^{2}+433a+287\right){x}+9624a^{3}-32279a^{2}+18906a+12022$ |
| 9.2-b3 |
9.2-b |
$4$ |
$4$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{8} \) |
$13.92145$ |
$(-a^3+5a), (-a^3-a^2+4a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$313.6077058$ |
0.662309787 |
\( \frac{8033730533}{3} a^{3} + \frac{29802495703}{9} a^{2} - \frac{81124261510}{9} a - \frac{33140563763}{9} \) |
\( \bigl[a^{3} - 4 a + 2\) , \( -a^{3} + a^{2} + 6 a - 5\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 18 a^{3} + 3 a^{2} - 96 a - 29\) , \( 86 a^{3} + 42 a^{2} - 432 a - 165\bigr] \) |
${y}^2+\left(a^{3}-4a+2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-5\right){x}^{2}+\left(18a^{3}+3a^{2}-96a-29\right){x}+86a^{3}+42a^{2}-432a-165$ |
| 9.2-b4 |
9.2-b |
$4$ |
$4$ |
4.4.14013.1 |
$4$ |
$[4, 0]$ |
9.2 |
\( 3^{2} \) |
\( 3^{4} \) |
$13.92145$ |
$(-a^3+5a), (-a^3-a^2+4a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$1254.430823$ |
0.662309787 |
\( -\frac{56596}{3} a^{3} - 30615 a^{2} + \frac{203077}{3} a + \frac{172117}{3} \) |
\( \bigl[a^{3} - 4 a + 2\) , \( -a^{3} + a^{2} + 6 a - 5\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 8 a^{3} + 3 a^{2} - 41 a - 9\) , \( -10 a^{3} - 5 a^{2} + 52 a + 17\bigr] \) |
${y}^2+\left(a^{3}-4a+2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}+a^{2}+6a-5\right){x}^{2}+\left(8a^{3}+3a^{2}-41a-9\right){x}-10a^{3}-5a^{2}+52a+17$ |
*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.
