| 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 |
| 3969.1-CMa1 |
3969.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{12} \cdot 7^{6} \) |
$1.87654$ |
$(-2a+1), (3)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{yes}$ |
$-7$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$0.336279925$ |
$1.648168200$ |
1.675882015 |
\( -3375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -20\) , \( 46\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-20{x}+46$ |
| 3969.1-CMa2 |
3969.1-CMa |
$2$ |
$2$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{12} \cdot 7^{6} \) |
$1.87654$ |
$(-2a+1), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{yes}$ |
$-28$ |
$\mathrm{U}(1)$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.336279925$ |
$0.824084100$ |
1.675882015 |
\( 16581375 \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -335\) , \( 2440\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-335{x}+2440$ |
| 3969.1-a1 |
3969.1-a |
$2$ |
$13$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{38} \cdot 7^{4} \) |
$1.87654$ |
$(-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$13$ |
13B.4.2 |
$1$ |
\( 2^{2} \) |
$0.991510447$ |
$0.138985368$ |
0.833368998 |
\( -\frac{1713910976512}{1594323} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -8211\) , \( -286610\bigr] \) |
${y}^2+{y}={x}^{3}-8211{x}-286610$ |
| 3969.1-a2 |
3969.1-a |
$2$ |
$13$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{14} \cdot 7^{4} \) |
$1.87654$ |
$(-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$13$ |
13B.4.1 |
$1$ |
\( 2^{2} \) |
$0.076270034$ |
$1.806809791$ |
0.833368998 |
\( -\frac{28672}{3} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -21\) , \( 40\bigr] \) |
${y}^2+{y}={x}^{3}-21{x}+40$ |
| 3969.1-b1 |
3969.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{6} \cdot 7^{8} \) |
$1.87654$ |
$(-2a+1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 7$ |
3B.1.1, 7Cn.0.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.894275780$ |
$2.215892550$ |
1.997284256 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 12\bigr] \) |
${y}^2+{y}={x}^{3}+12$ |
| 3969.1-b2 |
3969.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3969.1 |
\( 3^{4} \cdot 7^{2} \) |
\( 3^{18} \cdot 7^{8} \) |
$1.87654$ |
$(-2a+1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$3, 7$ |
3B.1.2, 7Cn.0.1[2] |
$1$ |
\( 2 \cdot 3 \) |
$0.298091926$ |
$0.738630850$ |
1.997284256 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -331\bigr] \) |
${y}^2+{y}={x}^{3}-331$ |
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*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.
