| 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 |
| 1125.11-a1 |
1125.11-a |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1125.11 |
\( 3^{2} \cdot 5^{3} \) |
\( 3^{3} \cdot 5^{5} \) |
$1.71642$ |
$(a-1), (-a-1), (a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.183441322$ |
$5.384904826$ |
2.382697164 |
\( \frac{21427}{125} a + \frac{54716}{125} \) |
\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -1\) , \( -a\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}-{x}-a$ |
| 1125.11-b1 |
1125.11-b |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1125.11 |
\( 3^{2} \cdot 5^{3} \) |
\( 3^{3} \cdot 5^{11} \) |
$1.71642$ |
$(a-1), (-a-1), (a-2)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.502050424$ |
$2.408202648$ |
2.916312187 |
\( \frac{21427}{125} a + \frac{54716}{125} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -5\) , \( 2 a + 7\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-5{x}+2a+7$ |
| 5625.13-b1 |
5625.13-b |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5625.13 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{3} \cdot 5^{11} \) |
$2.56664$ |
$(a-1), (-a-1), (a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{3} \) |
$0.108653280$ |
$2.408202648$ |
2.524582154 |
\( \frac{21427}{125} a + \frac{54716}{125} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -a + 7\) , \( -2 a + 4\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-a+7\right){x}-2a+4$ |
| 5625.13-g1 |
5625.13-g |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
5625.13 |
\( 3^{2} \cdot 5^{4} \) |
\( 3^{3} \cdot 5^{17} \) |
$2.56664$ |
$(a-1), (-a-1), (a-2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.076980965$ |
2.597775831 |
\( \frac{21427}{125} a + \frac{54716}{125} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -17 a - 2\) , \( 6 a - 104\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-17a-2\right){x}+6a-104$ |
| 10125.11-b2 |
10125.11-b |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
10125.11 |
\( 3^{4} \cdot 5^{3} \) |
\( 3^{15} \cdot 5^{11} \) |
$2.97292$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$1$ |
\( 2 \) |
$1.998723058$ |
$0.802734216$ |
3.870063065 |
\( \frac{21427}{125} a + \frac{54716}{125} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 12 a - 54\) , \( -87 a - 121\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(12a-54\right){x}-87a-121$ |
| 10125.11-f2 |
10125.11-f |
$2$ |
$3$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
10125.11 |
\( 3^{4} \cdot 5^{3} \) |
\( 3^{15} \cdot 5^{5} \) |
$2.97292$ |
$(-a), (a-1), (-a-1), (a-2)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3 \) |
$0.400800854$ |
$1.794968275$ |
5.205953861 |
\( \frac{21427}{125} a + \frac{54716}{125} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -6 a\) , \( a + 19\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-6a{x}+a+19$ |
*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.
