| 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 |
| 1089.2-b1 |
1089.2-b |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1089.2 |
\( 3^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 11^{4} \) |
$1.70252$ |
$(-a), (a-1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$3.570911540$ |
2.153340679 |
\( \frac{45056}{27} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 4\) , \( -1\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+4{x}-1$ |
| 3267.2-d1 |
3267.2-d |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3267.2 |
\( 3^{3} \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{10} \) |
$2.24064$ |
$(-a), (a-1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.621615910$ |
2.249090988 |
\( \frac{45056}{27} \) |
\( \bigl[0\) , \( a\) , \( 1\) , \( -40 a + 120\) , \( -18 a + 124\bigr] \) |
${y}^2+{y}={x}^{3}+a{x}^{2}+\left(-40a+120\right){x}-18a+124$ |
| 3267.3-e1 |
3267.3-e |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
3267.3 |
\( 3^{3} \cdot 11^{2} \) |
\( 3^{12} \cdot 11^{10} \) |
$2.24064$ |
$(-a), (a-1), (-2a+1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$0.621615910$ |
2.249090988 |
\( \frac{45056}{27} \) |
\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( 40 a + 80\) , \( 18 a + 106\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(40a+80\right){x}+18a+106$ |
| 9801.3-g1 |
9801.3-g |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9801.3 |
\( 3^{4} \cdot 11^{2} \) |
\( 3^{18} \cdot 11^{4} \) |
$2.94885$ |
$(-a), (a-1), (-2a+1)$ |
$2$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{4} \cdot 3 \) |
$0.030136233$ |
$1.190303846$ |
4.153188958 |
\( \frac{45056}{27} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( 33\) , \( -14\bigr] \) |
${y}^2+{y}={x}^{3}+33{x}-14$ |
| 27225.4-d1 |
27225.4-d |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.4 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{6} \cdot 11^{4} \) |
$3.80695$ |
$(-a), (a-1), (-a-1), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \cdot 3^{2} \) |
$0.107600940$ |
$1.596960189$ |
3.730321925 |
\( \frac{45056}{27} \) |
\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 12 a - 8\) , \( -3 a + 8\bigr] \) |
${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(12a-8\right){x}-3a+8$ |
| 27225.6-e1 |
27225.6-e |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
27225.6 |
\( 3^{2} \cdot 5^{2} \cdot 11^{2} \) |
\( 3^{6} \cdot 5^{6} \cdot 11^{4} \) |
$3.80695$ |
$(-a), (a-1), (a-2), (-2a+1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 2 \cdot 3^{2} \) |
$0.107600940$ |
$1.596960189$ |
3.730321925 |
\( \frac{45056}{27} \) |
\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -10 a + 3\) , \( -8 a + 8\bigr] \) |
${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-10a+3\right){x}-8a+8$ |
*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.
