| 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 |
| 180.3-a1 |
180.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
180.3 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{2} \cdot 3^{16} \cdot 5^{4} \) |
$1.08556$ |
$(-a), (a-1), (-a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.869937479$ |
1.049184077 |
\( \frac{1040615197465123}{664301250} a - \frac{4418354028130441}{664301250} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -30 a - 246\) , \( 378 a + 1584\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-30a-246\right){x}+378a+1584$ |
| 180.3-a2 |
180.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
180.3 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{2} \cdot 3^{4} \cdot 5^{16} \) |
$1.08556$ |
$(-a), (a-1), (-a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$0.869937479$ |
1.049184077 |
\( -\frac{86954837738674193}{8239746093750} a + \frac{30851593729206131}{8239746093750} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 30 a - 106\) , \( 174 a - 296\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(30a-106\right){x}+174a-296$ |
| 180.3-a3 |
180.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
180.3 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{8} \cdot 3^{4} \cdot 5^{4} \) |
$1.08556$ |
$(-a), (a-1), (-a-1), (2)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.479749919$ |
1.049184077 |
\( -\frac{198097073}{270000} a + \frac{225541091}{270000} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+4{x}$ |
| 180.3-a4 |
180.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
180.3 |
\( 2^{2} \cdot 3^{2} \cdot 5 \) |
\( 2^{4} \cdot 3^{8} \cdot 5^{8} \) |
$1.08556$ |
$(-a), (a-1), (-a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.739874959$ |
1.049184077 |
\( \frac{1649344256987}{1139062500} a + \frac{317245124723}{569531250} \) |
\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -16\) , \( 12 a + 28\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-16{x}+12a+28$ |
*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.
