| 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 |
| 56.1-b2 |
56.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$1.82928$ |
$(-a+4), (-2a+7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.933057233$ |
$24.47471212$ |
3.161100443 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -30 a + 112\) , \( -944 a + 3532\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-30a+112\right){x}-944a+3532$ |
| 56.1-d2 |
56.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
56.1 |
\( 2^{3} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$1.82928$ |
$(-a+4), (-2a+7)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.022709596$ |
$10.54517411$ |
2.850317744 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$ |
| 112.1-b2 |
112.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
112.1 |
\( 2^{4} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$2.17539$ |
$(-a+4), (-2a+7)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$10.54517411$ |
2.818316330 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( -30 a + 119\) , \( 854 a - 3192\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-30a+119\right){x}+854a-3192$ |
| 112.1-e2 |
112.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
112.1 |
\( 2^{4} \cdot 7 \) |
\( 2^{4} \cdot 7^{2} \) |
$2.17539$ |
$(-a+4), (-2a+7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.696738583$ |
$24.47471212$ |
2.278732990 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 7\) , \( 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+{x}^{2}+7{x}+4$ |
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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.
