| 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-j4 |
7425.5-j |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
7425.5 |
\( 3^{3} \cdot 5^{2} \cdot 11 \) |
\( 3^{18} \cdot 5^{9} \cdot 11^{3} \) |
$2.75112$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \cdot 3 \) |
$0.157762452$ |
$0.314224015$ |
5.739550825 |
\( \frac{4414177947758597}{310109765625} a + \frac{66272309919419452}{310109765625} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 736 a - 684\) , \( -9866 a - 3009\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(736a-684\right){x}-9866a-3009$ |
| 7425.8-i4 |
7425.8-i |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
7425.8 |
\( 3^{3} \cdot 5^{2} \cdot 11 \) |
\( 3^{18} \cdot 5^{9} \cdot 11^{3} \) |
$2.75112$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.314224015$ |
3.031747373 |
\( \frac{4414177947758597}{310109765625} a + \frac{66272309919419452}{310109765625} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 113 a - 1307\) , \( -2768 a + 17682\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(113a-1307\right){x}-2768a+17682$ |
| 27225.5-f4 |
27225.5-f |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.5 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{12} \cdot 5^{9} \cdot 11^{9} \) |
$3.80695$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.164098140$ |
1.583278428 |
\( \frac{4414177947758597}{310109765625} a + \frac{66272309919419452}{310109765625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 1870 a - 4375\) , \( 65725 a - 89110\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(1870a-4375\right){x}+65725a-89110$ |
| 37125.10-h4 |
37125.10-h |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.10 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{18} \cdot 5^{15} \cdot 11^{3} \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{9} \cdot 3 \) |
$0.104276369$ |
$0.140525251$ |
6.786332711 |
\( \frac{4414177947758597}{310109765625} a + \frac{66272309919419452}{310109765625} \) |
\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -3805 a + 1602\) , \( 88504 a - 171102\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-3805a+1602\right){x}+88504a-171102$ |
| 37125.11-b4 |
37125.11-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.11 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{18} \cdot 5^{15} \cdot 11^{3} \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.890691903$ |
$0.140525251$ |
3.622903507 |
\( \frac{4414177947758597}{310109765625} a + \frac{66272309919419452}{310109765625} \) |
\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 3693 a - 296\) , \( -43974 a - 156697\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3693a-296\right){x}-43974a-156697$ |
| 37125.6-a4 |
37125.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.6 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{18} \cdot 5^{15} \cdot 11^{3} \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.140525251$ |
1.355838643 |
\( \frac{4414177947758597}{310109765625} a + \frac{66272309919419452}{310109765625} \) |
\( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -1311 a - 5274\) , \( 60976 a + 137018\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1311a-5274\right){x}+60976a+137018$ |
| 37125.7-g4 |
37125.7-g |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.7 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{18} \cdot 5^{15} \cdot 11^{3} \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.140525251$ |
1.355838643 |
\( \frac{4414177947758597}{310109765625} a + \frac{66272309919419452}{310109765625} \) |
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 573 a + 5958\) , \( 113455 a - 101543\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(573a+5958\right){x}+113455a-101543$ |
*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.
