| 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 |
| 96.1-a1 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{8} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.261257214$ |
0.941443865 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 3 a - 9\) , \( -27\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(3a-9\right){x}-27$ |
| 96.1-a2 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{6} \cdot 3 \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$26.09005771$ |
0.941443865 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 50243 a - 87023\) , \( -8019946 a + 13890954\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(50243a-87023\right){x}-8019946a+13890954$ |
| 96.1-a3 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$26.09005771$ |
0.941443865 |
\( -\frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 920 a - 1591\) , \( -18385 a + 31843\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(920a-1591\right){x}-18385a+31843$ |
| 96.1-a4 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$26.09005771$ |
0.941443865 |
\( \frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -3102 a + 5373\) , \( -535777 a + 927993\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-3102a+5373\right){x}-535777a+927993$ |
| 96.1-a5 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{4} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$13.04502885$ |
0.941443865 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 56 a - 90\) , \( 222 a - 381\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(56a-90\right){x}+222a-381$ |
| 96.1-a6 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{2} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.261257214$ |
0.941443865 |
\( \frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -109 a + 195\) , \( 1392 a - 2409\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-109a+195\right){x}+1392a-2409$ |
| 96.1-b1 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.988372149$ |
1.297359770 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 97256 a - 168452\) , \( 21662226 a - 37520076\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(97256a-168452\right){x}+21662226a-37520076$ |
| 96.1-b2 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{2} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$17.97674429$ |
1.297359770 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 9135 a - 15826\) , \( -619924 a + 1073738\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(9135a-15826\right){x}-619924a+1073738$ |
| 96.1-b3 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{4} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$35.95348859$ |
1.297359770 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 570 a - 991\) , \( -9409 a + 16295\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(570a-991\right){x}-9409a+16295$ |
| 96.1-b4 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$17.97674429$ |
1.297359770 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 2720 a - 4711\) , \( -10125 a + 17537\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(2720a-4711\right){x}-10125a+17537$ |
| 96.1-b5 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{8} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$17.97674429$ |
1.297359770 |
\( \frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -3 a - 12\) , \( -3 a + 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-3a-12\right){x}-3a+16$ |
| 96.1-b6 |
96.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{6} \cdot 3 \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.988372149$ |
1.297359770 |
\( \frac{132636728}{3} a + 76579552 \) |
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -37569 a + 65072\) , \( -632444 a + 1095425\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-37569a+65072\right){x}-632444a+1095425$ |
| 96.1-c1 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{8} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$17.97674429$ |
1.297359770 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( a - 12\) , \( 2 a + 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(a-12\right){x}+2a+16$ |
| 96.1-c2 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{6} \cdot 3 \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.988372149$ |
1.297359770 |
\( -\frac{132636728}{3} a + 76579552 \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 50243 a - 87026\) , \( 8070189 a - 13977979\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(50243a-87026\right){x}+8070189a-13977979$ |
| 96.1-c3 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$17.97674429$ |
1.297359770 |
\( -\frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 920 a - 1591\) , \( 18385 a - 31843\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(920a-1591\right){x}+18385a-31843$ |
| 96.1-c4 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$8.988372149$ |
1.297359770 |
\( \frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -3102 a + 5373\) , \( 535777 a - 927993\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3102a+5373\right){x}+535777a-927993$ |
| 96.1-c5 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{4} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$35.95348859$ |
1.297359770 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 55 a - 91\) , \( -260 a + 452\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(55a-91\right){x}-260a+452$ |
| 96.1-c6 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{2} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$17.97674429$ |
1.297359770 |
\( \frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -110 a + 194\) , \( -1310 a + 2270\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-110a+194\right){x}-1310a+2270$ |
| 96.1-d1 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{12} \cdot 3 \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$26.09005771$ |
0.941443865 |
\( -\frac{166016}{3} a + 95936 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 97256 a - 168452\) , \( -21662226 a + 37520076\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(97256a-168452\right){x}-21662226a+37520076$ |
| 96.1-d2 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{2} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.261257214$ |
0.941443865 |
\( -\frac{164847992914}{3} a + \frac{285525100658}{3} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 9137 a - 15823\) , \( 629060 a - 1089563\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(9137a-15823\right){x}+629060a-1089563$ |
| 96.1-d3 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{4} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$13.04502885$ |
0.941443865 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 572 a - 988\) , \( 9980 a - 17285\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(572a-988\right){x}+9980a-17285$ |
| 96.1-d4 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$26.09005771$ |
0.941443865 |
\( \frac{9856}{3} a + \frac{22336}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2720 a - 4711\) , \( 10125 a - 17537\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(2720a-4711\right){x}+10125a-17537$ |
| 96.1-d5 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{8} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.261257214$ |
0.941443865 |
\( \frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -3 a - 9\) , \( -27\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-9\right){x}-27$ |
| 96.1-d6 |
96.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{6} \cdot 3 \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$26.09005771$ |
0.941443865 |
\( \frac{132636728}{3} a + 76579552 \) |
\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -37568 a + 65073\) , \( 659947 a - 1143060\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-37568a+65073\right){x}+659947a-1143060$ |
*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.
