| 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 |
| 275.2-a1 |
275.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
275.2 |
\( 5^{2} \cdot 11 \) |
\( 5^{2} \cdot 11^{2} \) |
$1.20689$ |
$(-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.409696668$ |
$7.082488443$ |
1.505168807 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+{x}$ |
| 1375.2-a1 |
1375.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1375.2 |
\( 5^{3} \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$1.80472$ |
$(-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.167385122$ |
1.910005093 |
\( \frac{59319}{55} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 3 a - 2\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(3a-2\right){x}$ |
| 1375.3-a1 |
1375.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1375.3 |
\( 5^{3} \cdot 11 \) |
\( 5^{8} \cdot 11^{2} \) |
$1.80472$ |
$(-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.167385122$ |
1.910005093 |
\( \frac{59319}{55} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -3 a + 1\) , \( 0\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-3a+1\right){x}$ |
| 6875.3-a1 |
6875.3-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6875.3 |
\( 5^{4} \cdot 11 \) |
\( 5^{14} \cdot 11^{2} \) |
$2.69869$ |
$(-a-1), (a-2), (-2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.596122623$ |
$1.416497688$ |
2.036784674 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 20\) , \( 22\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+20{x}+22$ |
| 22275.8-a1 |
22275.8-a |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
22275.8 |
\( 3^{4} \cdot 5^{2} \cdot 11 \) |
\( 3^{12} \cdot 5^{2} \cdot 11^{2} \) |
$3.62067$ |
$(-a), (a-1), (-a-1), (a-2), (-2a+1)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.496724502$ |
$2.360829481$ |
5.657230102 |
\( \frac{59319}{55} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( 7\) , \( -8\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+7{x}-8$ |
| 27225.2-b1 |
27225.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.2 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{2} \cdot 11^{8} \) |
$3.80695$ |
$(-a), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.232902986$ |
1.486936948 |
\( \frac{59319}{55} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -11 a + 28\) , \( -11 a + 30\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-11a+28\right){x}-11a+30$ |
| 27225.8-b1 |
27225.8-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.8 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{2} \cdot 11^{8} \) |
$3.80695$ |
$(a-1), (-a-1), (a-2), (-2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.232902986$ |
1.486936948 |
\( \frac{59319}{55} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 9 a + 19\) , \( 10 a + 20\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(9a+19\right){x}+10a+20$ |
*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.
