| 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 |
| 882.2-a4 |
882.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
882.2 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \) |
$1.37737$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.141519658$ |
$0.342545916$ |
2.211959540 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-914{x}-10915$ |
| 7056.2-f4 |
7056.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7056.2 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{14} \cdot 3^{8} \cdot 7^{16} \) |
$2.31645$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{9} \) |
$1$ |
$0.171272958$ |
3.875464647 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -3655\) , \( -83662\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-3655{x}-83662$ |
| 7938.3-a4 |
7938.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{2} \cdot 3^{20} \cdot 7^{16} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.114181972$ |
1.291821549 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -8226\) , \( 286474\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-8226{x}+286474$ |
| 43218.2-f4 |
43218.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
43218.2 |
\( 2 \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{2} \cdot 3^{8} \cdot 7^{28} \) |
$3.64418$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{7} \) |
$1$ |
$0.048935130$ |
4.429102453 |
\( \frac{84448510979617}{933897762} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -44787\) , \( 3609423\bigr] \) |
${y}^2+{x}{y}={x}^{3}-44787{x}+3609423$ |
*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.
