| 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-g2 |
7425.5-g |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
7425.5 |
\( 3^{3} \cdot 5^{2} \cdot 11 \) |
\( 3^{18} \cdot 5^{5} \cdot 11 \) |
$2.75112$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.133079532$ |
$0.901139608$ |
4.628251749 |
\( \frac{156915268913}{45106875} a - \frac{780192126332}{15035625} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 5 a + 117\) , \( -294 a + 182\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(5a+117\right){x}-294a+182$ |
| 7425.8-b2 |
7425.8-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
7425.8 |
\( 3^{3} \cdot 5^{2} \cdot 11 \) |
\( 3^{18} \cdot 5^{5} \cdot 11 \) |
$2.75112$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.698601190$ |
$0.901139608$ |
3.037001738 |
\( \frac{156915268913}{45106875} a - \frac{780192126332}{15035625} \) |
\( \bigl[1\) , \( a + 1\) , \( 0\) , \( 69 a + 3\) , \( 144 a + 369\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(69a+3\right){x}+144a+369$ |
| 27225.5-j2 |
27225.5-j |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.5 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{12} \cdot 5^{5} \cdot 11^{7} \) |
$3.80695$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.403708938$ |
$0.470604812$ |
3.666134217 |
\( \frac{156915268913}{45106875} a - \frac{780192126332}{15035625} \) |
\( \bigl[a + 1\) , \( a\) , \( a\) , \( 161 a + 260\) , \( 1378 a - 3886\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(161a+260\right){x}+1378a-3886$ |
| 37125.10-c2 |
37125.10-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.10 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{18} \cdot 5^{11} \cdot 11 \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.260132730$ |
$0.403001884$ |
4.899784783 |
\( \frac{156915268913}{45106875} a - \frac{780192126332}{15035625} \) |
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 77 a - 615\) , \( 1010 a - 5554\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(77a-615\right){x}+1010a-5554$ |
| 37125.11-q2 |
37125.11-q |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.11 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{18} \cdot 5^{11} \cdot 11 \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$0.562339546$ |
$0.403001884$ |
8.746198515 |
\( \frac{156915268913}{45106875} a - \frac{780192126332}{15035625} \) |
\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -146 a + 614\) , \( -2767 a - 2089\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-146a+614\right){x}-2767a-2089$ |
| 37125.6-h2 |
37125.6-h |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.6 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{18} \cdot 5^{11} \cdot 11 \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.412022515$ |
$0.403001884$ |
5.490379120 |
\( \frac{156915268913}{45106875} a - \frac{780192126332}{15035625} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 351 a - 279\) , \( 2781 a + 1532\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(351a-279\right){x}+2781a+1532$ |
| 37125.7-i2 |
37125.7-i |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
37125.7 |
\( 3^{3} \cdot 5^{3} \cdot 11 \) |
\( 3^{18} \cdot 5^{11} \cdot 11 \) |
$4.11388$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$0.229925589$ |
$0.403001884$ |
7.152172951 |
\( \frac{156915268913}{45106875} a - \frac{780192126332}{15035625} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -358 a + 165\) , \( 2506 a - 4793\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-358a+165\right){x}+2506a-4793$ |
*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.
