| 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 |
| 3564.3-b4 |
3564.3-b |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3564.3 |
\( 2^{2} \cdot 3^{4} \cdot 11 \) |
\( 2^{12} \cdot 3^{6} \cdot 11^{4} \) |
$2.28991$ |
$(-a), (a-1), (-2a+1), (2)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$4$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.571141624$ |
1.836860576 |
\( \frac{4406910829875}{7744} \) |
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1025\) , \( 12881\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-1025{x}+12881$ |
| 3564.3-d4 |
3564.3-d |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3564.3 |
\( 2^{2} \cdot 3^{4} \cdot 11 \) |
\( 2^{12} \cdot 3^{18} \cdot 11^{4} \) |
$2.28991$ |
$(-a), (a-1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.743066361$ |
$0.190380541$ |
4.094727914 |
\( \frac{4406910829875}{7744} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -9222\) , \( -338572\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-9222{x}-338572$ |
| 39204.3-l4 |
39204.3-l |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
39204.3 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 11^{10} \) |
$4.17030$ |
$(-a), (a-1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$2.288950724$ |
$0.099422995$ |
6.587159449 |
\( \frac{4406910829875}{7744} \) |
\( \bigl[a + 1\) , \( -1\) , \( a\) , \( 11270 a - 33813\) , \( -1122280 a + 2091595\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-{x}^{2}+\left(11270a-33813\right){x}-1122280a+2091595$ |
| 39204.3-m4 |
39204.3-m |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
39204.3 |
\( 2^{2} \cdot 3^{4} \cdot 11^{2} \) |
\( 2^{12} \cdot 3^{12} \cdot 11^{10} \) |
$4.17030$ |
$(-a), (a-1), (-2a+1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \cdot 3 \) |
$2.288950724$ |
$0.099422995$ |
6.587159449 |
\( \frac{4406910829875}{7744} \) |
\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -11272 a - 22542\) , \( 1122279 a + 969315\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-11272a-22542\right){x}+1122279a+969315$ |
*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.
