| 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 |
| 400.2-a1 |
400.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
400.2 |
\( 2^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{12} \) |
$1.32541$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.242753107$ |
$1.070515942$ |
0.940248913 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -36\) , \( -140\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-36{x}-140$ |
| 2000.2-a1 |
2000.2-a |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2000.2 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{16} \cdot 5^{18} \) |
$1.98195$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.478749283$ |
1.732180083 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -108 a + 72\) , \( -560 a + 1540\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-108a+72\right){x}-560a+1540$ |
| 2000.3-a1 |
2000.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
2000.3 |
\( 2^{4} \cdot 5^{3} \) |
\( 2^{16} \cdot 5^{18} \) |
$1.98195$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.478749283$ |
1.732180083 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 110 a - 37\) , \( 451 a + 1017\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(110a-37\right){x}+451a+1017$ |
| 6400.2-w1 |
6400.2-w |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6400.2 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{16} \cdot 5^{12} \) |
$2.65082$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \) |
$5.403236659$ |
$1.070515942$ |
6.976069169 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -36\) , \( 140\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-36{x}+140$ |
| 10000.3-a1 |
10000.3-a |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
10000.3 |
\( 2^{4} \cdot 5^{4} \) |
\( 2^{16} \cdot 5^{24} \) |
$2.96370$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{4} \cdot 3 \) |
$2.823282594$ |
$0.214103188$ |
8.748274076 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -908\) , \( -15688\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-908{x}-15688$ |
| 32000.2-bb1 |
32000.2-bb |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
32000.2 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{16} \cdot 5^{18} \) |
$3.96390$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.478749283$ |
1.732180083 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -108 a + 72\) , \( 560 a - 1540\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-108a+72\right){x}+560a-1540$ |
| 32000.3-h1 |
32000.3-h |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
32000.3 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{16} \cdot 5^{18} \) |
$3.96390$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$0.478749283$ |
1.732180083 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 110 a - 37\) , \( -451 a - 1017\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(110a-37\right){x}-451a-1017$ |
| 32400.8-e1 |
32400.8-e |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
32400.8 |
\( 2^{4} \cdot 3^{4} \cdot 5^{2} \) |
\( 2^{16} \cdot 3^{12} \cdot 5^{12} \) |
$3.97623$ |
$(-a), (a-1), (-a-1), (a-2), (2)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{4} \cdot 3^{3} \) |
$1.244324699$ |
$0.356838647$ |
6.426144713 |
\( -\frac{20720464}{15625} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -327\) , \( 3454\bigr] \) |
${y}^2={x}^{3}-327{x}+3454$ |
*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.
