| 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-f5 |
7425.5-f |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
7425.5 |
\( 3^{3} \cdot 5^{2} \cdot 11 \) |
\( 3^{19} \cdot 5^{2} \cdot 11^{3} \) |
$2.75112$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$1$ |
$1.027176232$ |
1.238821148 |
\( -\frac{14695715479}{321521805} a + \frac{31276588903}{107173935} \) |
\( \bigl[1\) , \( a - 1\) , \( 0\) , \( -6 a - 21\) , \( 41 a - 89\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6a-21\right){x}+41a-89$ |
| 7425.8-h5 |
7425.8-h |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
7425.8 |
\( 3^{3} \cdot 5^{2} \cdot 11 \) |
\( 3^{19} \cdot 5^{2} \cdot 11^{3} \) |
$2.75112$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$4.223398900$ |
$1.027176232$ |
5.232035875 |
\( -\frac{14695715479}{321521805} a + \frac{31276588903}{107173935} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -16 a + 9\) , \( -51 a - 42\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-16a+9\right){x}-51a-42$ |
| 27225.5-d5 |
27225.5-d |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.5 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{13} \cdot 5^{2} \cdot 11^{9} \) |
$3.80695$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$4.983701257$ |
$0.536425292$ |
3.224221700 |
\( -\frac{14695715479}{321521805} a + \frac{31276588903}{107173935} \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -46 a - 26\) , \( 75 a + 740\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-46a-26\right){x}+75a+740$ |
| 37125.10-j5 |
37125.10-j |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.10 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{19} \cdot 5^{8} \cdot 11^{3} \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.459367176$ |
3.324105959 |
\( -\frac{14695715479}{321521805} a + \frac{31276588903}{107173935} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( 7 a + 120\) , \( 184 a + 1080\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(7a+120\right){x}+184a+1080$ |
| 37125.11-g5 |
37125.11-g |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.11 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{19} \cdot 5^{8} \cdot 11^{3} \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1.428862057$ |
$0.459367176$ |
4.749688881 |
\( -\frac{14695715479}{321521805} a + \frac{31276588903}{107173935} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 7 a - 126\) , \( 729 a - 309\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(7a-126\right){x}+729a-309$ |
| 37125.6-i5 |
37125.6-i |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.6 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{19} \cdot 5^{8} \cdot 11^{3} \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \) |
$5.232267347$ |
$0.459367176$ |
5.797537023 |
\( -\frac{14695715479}{321521805} a + \frac{31276588903}{107173935} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -67 a + 93\) , \( -711 a + 581\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-67a+93\right){x}-711a+581$ |
| 37125.7-k5 |
37125.7-k |
$8$ |
$12$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.7 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{19} \cdot 5^{8} \cdot 11^{3} \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \cdot 3 \) |
$1$ |
$0.459367176$ |
3.324105959 |
\( -\frac{14695715479}{321521805} a + \frac{31276588903}{107173935} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 70 a - 74\) , \( -169 a + 1191\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(70a-74\right){x}-169a+1191$ |
*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.
