| 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 |
| 1600.2-c4 |
1600.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1600.2 |
\( 2^{6} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{2} \) |
$1.87441$ |
$(-a-1), (a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.498444490$ |
1.807192052 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( -426\bigr] \) |
${y}^2={x}^{3}-107{x}-426$ |
| 6400.2-k4 |
6400.2-k |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
6400.2 |
\( 2^{8} \cdot 5^{2} \) |
\( 2^{20} \cdot 5^{2} \) |
$2.65082$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$2.178039125$ |
$1.498444490$ |
3.936134998 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -107\) , \( 426\bigr] \) |
${y}^2={x}^{3}-107{x}+426$ |
| 8000.2-b4 |
8000.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
8000.2 |
\( 2^{6} \cdot 5^{3} \) |
\( 2^{20} \cdot 5^{8} \) |
$2.80290$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.801455120$ |
$0.670124748$ |
3.072339281 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -321 a + 214\) , \( -1704 a + 4686\bigr] \) |
${y}^2={x}^{3}+\left(-321a+214\right){x}-1704a+4686$ |
| 8000.3-c4 |
8000.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
8000.3 |
\( 2^{6} \cdot 5^{3} \) |
\( 2^{20} \cdot 5^{8} \) |
$2.80290$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.801455120$ |
$0.670124748$ |
3.072339281 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 321 a - 107\) , \( 1704 a + 2982\bigr] \) |
${y}^2={x}^{3}+\left(321a-107\right){x}+1704a+2982$ |
| 32000.2-s4 |
32000.2-s |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
32000.2 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{20} \cdot 5^{8} \) |
$3.96390$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.594152394$ |
$0.670124748$ |
4.193192370 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -321 a + 214\) , \( 1704 a - 4686\bigr] \) |
${y}^2={x}^{3}+\left(-321a+214\right){x}+1704a-4686$ |
| 32000.3-t4 |
32000.3-t |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
32000.3 |
\( 2^{8} \cdot 5^{3} \) |
\( 2^{20} \cdot 5^{8} \) |
$3.96390$ |
$(-a-1), (a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.594152394$ |
$0.670124748$ |
4.193192370 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 321 a - 107\) , \( -1704 a - 2982\bigr] \) |
${y}^2={x}^{3}+\left(321a-107\right){x}-1704a-2982$ |
| 40000.3-h4 |
40000.3-h |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
40000.3 |
\( 2^{6} \cdot 5^{4} \) |
\( 2^{20} \cdot 5^{14} \) |
$4.19131$ |
$(-a-1), (a-2), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.611369997$ |
$0.299688898$ |
9.318576171 |
\( \frac{132304644}{5} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2675\) , \( -53250\bigr] \) |
${y}^2={x}^{3}-2675{x}-53250$ |
*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.
