| 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-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-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 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 572 a - 988\) , \( 9980 a - 17285\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(572a-988\right){x}+9980a-17285$ |
| 288.1-a3 |
288.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 23873 a - 41349\) , \( 2630312 a - 4555834\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(23873a-41349\right){x}+2630312a-4555834$ |
| 288.1-c3 |
288.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 23873 a - 41349\) , \( -2630312 a + 4555834\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(23873a-41349\right){x}-2630312a+4555834$ |
| 768.1-a3 |
768.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2286 a - 3957\) , \( 77553 a - 134325\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(2286a-3957\right){x}+77553a-134325$ |
| 768.1-p3 |
768.1-p |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2286 a - 3957\) , \( -77553 a + 134325\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2286a-3957\right){x}-77553a+134325$ |
| 2304.1-u3 |
2304.1-u |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 95492 a - 165396\) , \( -21042496 a + 36446672\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(95492a-165396\right){x}-21042496a+36446672$ |
| 2304.1-x3 |
2304.1-x |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 95492 a - 165396\) , \( 21042496 a - 36446672\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(95492a-165396\right){x}+21042496a-36446672$ |
| 3072.1-s3 |
3072.1-s |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 17058 a - 29545\) , \( -1598538 a + 2768749\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(17058a-29545\right){x}-1598538a+2768749$ |
| 3072.1-ba3 |
3072.1-ba |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 1224 a - 2120\) , \( 29528 a - 51144\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(1224a-2120\right){x}+29528a-51144$ |
| 3072.1-be3 |
3072.1-be |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 17058 a - 29545\) , \( 1598538 a - 2768749\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(17058a-29545\right){x}+1598538a-2768749$ |
| 3072.1-bk3 |
3072.1-bk |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -\frac{1122088}{9} a + \frac{1989808}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 1224 a - 2120\) , \( -29528 a + 51144\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(1224a-2120\right){x}-29528a+51144$ |
*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.
