| 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 |
| 9075.5-a2 |
9075.5-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9075.5 |
\( 3 \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{10} \cdot 5^{9} \cdot 11^{9} \) |
$2.89265$ |
$(a-1), (-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$2.156535252$ |
$0.269437232$ |
7.007737416 |
\( \frac{17874017121802}{23066015625} a + \frac{4304613879119}{7688671875} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -347 a + 404\) , \( 1509 a + 5097\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-347a+404\right){x}+1509a+5097$ |
| 27225.8-c2 |
27225.8-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.8 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{16} \cdot 5^{9} \cdot 11^{3} \) |
$3.80695$ |
$(a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.515933021$ |
4.977909085 |
\( \frac{17874017121802}{23066015625} a + \frac{4304613879119}{7688671875} \) |
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -58 a + 168\) , \( -458 a - 55\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-58a+168\right){x}-458a-55$ |
| 45375.6-a2 |
45375.6-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
45375.6 |
\( 3 \cdot 5^{3} \cdot 11^{2} \) |
\( 3^{10} \cdot 5^{15} \cdot 11^{9} \) |
$4.32553$ |
$(a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.120495993$ |
1.162589090 |
\( \frac{17874017121802}{23066015625} a + \frac{4304613879119}{7688671875} \) |
\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 873 a + 2303\) , \( 8387 a - 66945\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(873a+2303\right){x}+8387a-66945$ |
| 45375.7-f2 |
45375.7-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
45375.7 |
\( 3 \cdot 5^{3} \cdot 11^{2} \) |
\( 3^{10} \cdot 5^{15} \cdot 11^{9} \) |
$4.32553$ |
$(a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 5 \) |
$1$ |
$0.120495993$ |
1.453236362 |
\( \frac{17874017121802}{23066015625} a + \frac{4304613879119}{7688671875} \) |
\( \bigl[a\) , \( 0\) , \( 1\) , \( -527 a - 2710\) , \( -33226 a - 16429\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(-527a-2710\right){x}-33226a-16429$ |
*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.
