| 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-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-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 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 55 a - 91\) , \( -260 a + 452\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(55a-91\right){x}-260a+452$ |
| 288.1-b5 |
288.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{10} \) |
$1.27520$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.04344473$ |
1.449646380 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 11 a - 21\) , \( -20 a + 34\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(11a-21\right){x}-20a+34$ |
| 288.1-d5 |
288.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{10} \) |
$1.27520$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.410195878$ |
$15.56618300$ |
1.843243885 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 11 a - 21\) , \( 20 a - 34\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(11a-21\right){x}+20a-34$ |
| 768.1-c5 |
768.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{18} \cdot 3^{4} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.423668005$ |
$17.97674429$ |
2.198599305 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 216 a - 374\) , \( -1926 a + 3336\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(216a-374\right){x}-1926a+3336$ |
| 768.1-n5 |
768.1-n |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{18} \cdot 3^{4} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$6.522514429$ |
1.882887730 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 216 a - 374\) , \( 1926 a - 3336\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(216a-374\right){x}+1926a-3336$ |
| 2304.1-b5 |
2304.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{10} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$5.021722368$ |
1.449646380 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 44 a - 84\) , \( -160 a + 272\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(44a-84\right){x}-160a+272$ |
| 2304.1-e5 |
2304.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{10} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$7.783091503$ |
2.246784987 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 44 a - 84\) , \( 160 a - 272\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(44a-84\right){x}+160a-272$ |
| 3072.1-b5 |
3072.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{24} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.060171480$ |
$9.532301402$ |
2.917314563 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 116 a - 200\) , \( 756 a - 1308\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(116a-200\right){x}+756a-1308$ |
| 3072.1-i5 |
3072.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{24} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$9.532301402$ |
2.751738390 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1612 a - 2792\) , \( 39276 a - 68028\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(1612a-2792\right){x}+39276a-68028$ |
| 3072.1-br5 |
3072.1-br |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{24} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$6.150328716$ |
1.775446970 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 116 a - 200\) , \( -756 a + 1308\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(116a-200\right){x}-756a+1308$ |
| 3072.1-cd5 |
3072.1-cd |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{24} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.869987237$ |
$6.150328716$ |
3.320063175 |
\( \frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1612 a - 2792\) , \( -39276 a + 68028\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(1612a-2792\right){x}-39276a+68028$ |
*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.
