| 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 |
| 7425.5-f2 |
7425.5-f |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
7425.5 |
\( 3^{3} \cdot 5^{2} \cdot 11 \) |
\( 3^{13} \cdot 5^{6} \cdot 11 \) |
$2.75112$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{3} \) |
$1$ |
$1.027176232$ |
1.238821148 |
\( -\frac{9627540947}{111375} a - \frac{3388012042}{7425} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 80 a - 60\) , \( 275 a + 75\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(80a-60\right){x}+275a+75$ |
| 7425.8-h2 |
7425.8-h |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
7425.8 |
\( 3^{3} \cdot 5^{2} \cdot 11 \) |
\( 3^{13} \cdot 5^{6} \cdot 11 \) |
$2.75112$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3^{3} \) |
$1.407799633$ |
$1.027176232$ |
5.232035875 |
\( -\frac{9627540947}{111375} a - \frac{3388012042}{7425} \) |
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 22 a - 141\) , \( 96 a - 666\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(22a-141\right){x}+96a-666$ |
| 27225.5-d2 |
27225.5-d |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.5 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{7} \cdot 5^{6} \cdot 11^{7} \) |
$3.80695$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$1.661233752$ |
$0.536425292$ |
3.224221700 |
\( -\frac{9627540947}{111375} a - \frac{3388012042}{7425} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 225 a - 437\) , \( -2363 a + 2243\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(225a-437\right){x}-2363a+2243$ |
| 37125.10-j2 |
37125.10-j |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.10 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{13} \cdot 5^{12} \cdot 11 \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.459367176$ |
3.324105959 |
\( -\frac{9627540947}{111375} a - \frac{3388012042}{7425} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -401 a + 86\) , \( -3426 a + 5057\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-401a+86\right){x}-3426a+5057$ |
| 37125.11-g2 |
37125.11-g |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.11 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{13} \cdot 5^{12} \cdot 11 \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$4.286586173$ |
$0.459367176$ |
4.749688881 |
\( -\frac{9627540947}{111375} a - \frac{3388012042}{7425} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 380 a + 54\) , \( 1226 a + 5766\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(380a+54\right){x}+1226a+5766$ |
| 37125.6-i2 |
37125.6-i |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.6 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{13} \cdot 5^{12} \cdot 11 \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1.744089115$ |
$0.459367176$ |
5.797537023 |
\( -\frac{9627540947}{111375} a - \frac{3388012042}{7425} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( -92 a - 612\) , \( -1113 a - 5620\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-92a-612\right){x}-1113a-5620$ |
| 37125.7-k2 |
37125.7-k |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.7 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{13} \cdot 5^{12} \cdot 11 \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.459367176$ |
3.324105959 |
\( -\frac{9627540947}{111375} a - \frac{3388012042}{7425} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( 11 a + 669\) , \( -4019 a + 2152\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(11a+669\right){x}-4019a+2152$ |
*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.
