| 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 |
| 6875.3-a1 |
6875.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6875.3 |
\( 5^{4} \cdot 11 \) |
\( 5^{14} \cdot 11^{2} \) |
$2.69869$ |
$(-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.596122623$ |
$1.416497688$ |
2.036784674 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 20\) , \( 22\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+20{x}+22$ |
| 6875.3-a2 |
6875.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6875.3 |
\( 5^{4} \cdot 11 \) |
\( 5^{16} \cdot 11^{4} \) |
$2.69869$ |
$(-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.192245246$ |
$0.708248844$ |
2.036784674 |
\( \frac{8120601}{3025} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -105\) , \( 272\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-105{x}+272$ |
| 6875.3-a3 |
6875.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6875.3 |
\( 5^{4} \cdot 11 \) |
\( 5^{14} \cdot 11^{8} \) |
$2.69869$ |
$(-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.596122623$ |
$0.354124422$ |
2.036784674 |
\( \frac{2749884201}{73205} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -730\) , \( -7228\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-730{x}-7228$ |
| 6875.3-a4 |
6875.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6875.3 |
\( 5^{4} \cdot 11 \) |
\( 5^{20} \cdot 11^{2} \) |
$2.69869$ |
$(-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.596122623$ |
$0.354124422$ |
2.036784674 |
\( \frac{22930509321}{6875} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1480\) , \( 22272\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-1480{x}+22272$ |
| 6875.3-b1 |
6875.3-b |
$3$ |
$25$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6875.3 |
\( 5^{4} \cdot 11 \) |
\( 5^{12} \cdot 11^{2} \) |
$2.69869$ |
$(-a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cn, 5B.1.3 |
$25$ |
\( 2 \) |
$1$ |
$0.074061744$ |
2.233045629 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -195508\) , \( -33338481\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-195508{x}-33338481$ |
| 6875.3-b2 |
6875.3-b |
$3$ |
$25$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6875.3 |
\( 5^{4} \cdot 11 \) |
\( 5^{12} \cdot 11^{10} \) |
$2.69869$ |
$(-a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cn, 5Cs.1.3 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$0.370308724$ |
2.233045629 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -258\) , \( -2981\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-258{x}-2981$ |
| 6875.3-b3 |
6875.3-b |
$3$ |
$25$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6875.3 |
\( 5^{4} \cdot 11 \) |
\( 5^{12} \cdot 11^{2} \) |
$2.69869$ |
$(-a-1), (a-2), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 5$ |
2Cn, 5B.1.4 |
$1$ |
\( 2 \) |
$1$ |
$1.851543623$ |
2.233045629 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -8\) , \( 19\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-8{x}+19$ |
*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.
