| 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 |
| 63.1-a1 |
63.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
63.1 |
\( 3^{2} \cdot 7 \) |
\( 3^{2} \cdot 7^{16} \) |
$0.66607$ |
$(-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$0.862076929$ |
0.325834452 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) |
${y}^2+{x}{y}={x}^{3}-34{x}-217$ |
| 567.1-a1 |
567.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
567.1 |
\( 3^{4} \cdot 7 \) |
\( 3^{14} \cdot 7^{16} \) |
$1.15367$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.638508823$ |
$0.287358976$ |
2.292578873 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -306\) , \( 5859\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-306{x}+5859$ |
| 4032.1-c1 |
4032.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.1 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{2} \cdot 7^{16} \) |
$1.88394$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.304790221$ |
1.843198006 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -170 a - 68\) , \( -3689 a + 1302\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-170a-68\right){x}-3689a+1302$ |
| 4032.7-c1 |
4032.7-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.7 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{18} \cdot 3^{2} \cdot 7^{16} \) |
$1.88394$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.304790221$ |
1.843198006 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 170 a - 238\) , \( 3689 a - 2387\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(170a-238\right){x}+3689a-2387$ |
| 7056.1-c1 |
7056.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7056.1 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{22} \) |
$2.16684$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.162917226$ |
1.970461553 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( -714 a + 476\) , \( 13671 a - 33418\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-714a+476\right){x}+13671a-33418$ |
| 7056.5-c1 |
7056.5-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
7056.5 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 7^{22} \) |
$2.16684$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.162917226$ |
1.970461553 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 714 a - 238\) , \( -13671 a - 19747\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(714a-238\right){x}-13671a-19747$ |
| 16128.5-i1 |
16128.5-i |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
16128.5 |
\( 2^{8} \cdot 3^{2} \cdot 7 \) |
\( 2^{24} \cdot 3^{2} \cdot 7^{16} \) |
$2.66430$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.746299208$ |
$0.215519232$ |
3.890719903 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -544\) , \( 13888\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-544{x}+13888$ |
| 28224.1-d1 |
28224.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28224.1 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{2} \cdot 7^{22} \) |
$3.06438$ |
$(a), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.943549961$ |
$0.115199875$ |
2.070326753 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1190 a + 476\) , \( 7595 a - 94178\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1190a+476\right){x}+7595a-94178$ |
| 28224.7-d1 |
28224.7-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
28224.7 |
\( 2^{6} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{18} \cdot 3^{2} \cdot 7^{22} \) |
$3.06438$ |
$(-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$5.943549961$ |
$0.115199875$ |
2.070326753 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -1190 a + 1665\) , \( -7119 a - 84202\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-1190a+1665\right){x}-7119a-84202$ |
| 36288.1-c1 |
36288.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.1 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{18} \cdot 3^{14} \cdot 7^{16} \) |
$3.26308$ |
$(a), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.101596740$ |
1.228798671 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -1530 a - 612\) , \( 99603 a - 35154\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1530a-612\right){x}+99603a-35154$ |
| 36288.7-c1 |
36288.7-c |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
36288.7 |
\( 2^{6} \cdot 3^{4} \cdot 7 \) |
\( 2^{18} \cdot 3^{14} \cdot 7^{16} \) |
$3.26308$ |
$(-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.101596740$ |
1.228798671 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 1530 a - 2143\) , \( -98073 a + 62306\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(1530a-2143\right){x}-98073a+62306$ |
| 39375.1-d1 |
39375.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
39375.1 |
\( 3^{2} \cdot 5^{4} \cdot 7 \) |
\( 3^{2} \cdot 5^{12} \cdot 7^{16} \) |
$3.33037$ |
$(-2a+1), (3), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.931482321$ |
$0.172415385$ |
8.055596601 |
\( -\frac{4354703137}{17294403} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -850\) , \( -27125\bigr] \) |
${y}^2+{x}{y}={x}^{3}+{x}^{2}-850{x}-27125$ |
*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.
