| 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 |
| 8320.2-b1 |
8320.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8320.2 |
\( 2^{7} \cdot 5 \cdot 13 \) |
\( 2^{16} \cdot 5^{2} \cdot 13 \) |
$1.70687$ |
$(a+1), (-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.185912591$ |
$3.385308722$ |
2.517486070 |
\( \frac{116352}{325} a + \frac{263936}{325} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 2 i + 3\) , \( 2 i + 3\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(2i+3\right){x}+2i+3$ |
| 16640.2-f1 |
16640.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16640.2 |
\( 2^{8} \cdot 5 \cdot 13 \) |
\( 2^{16} \cdot 5^{2} \cdot 13 \) |
$2.02982$ |
$(a+1), (-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.246010947$ |
$3.385308722$ |
3.331292019 |
\( \frac{116352}{325} a + \frac{263936}{325} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -2 i - 3\) , \( -3 i + 2\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-2i-3\right){x}-3i+2$ |
| 41600.2-d1 |
41600.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
41600.2 |
\( 2^{7} \cdot 5^{2} \cdot 13 \) |
\( 2^{16} \cdot 5^{8} \cdot 13 \) |
$2.55236$ |
$(a+1), (-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.332808813$ |
$1.513956085$ |
4.030863424 |
\( \frac{116352}{325} a + \frac{263936}{325} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -16 i\) , \( -16 i - 20\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}-16i{x}-16i-20$ |
| 66560.2-f1 |
66560.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.2 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{10} \cdot 5^{2} \cdot 13 \) |
$2.87059$ |
$(a+1), (-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$0.887845190$ |
$4.787549508$ |
4.250602806 |
\( \frac{116352}{325} a + \frac{263936}{325} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -2 i + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(-2i+1\right){x}$ |
| 66560.2-p1 |
66560.2-p |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.2 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{10} \cdot 5^{2} \cdot 13 \) |
$2.87059$ |
$(a+1), (-a-2), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.787549508$ |
2.393774754 |
\( \frac{116352}{325} a + \frac{263936}{325} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 2 i - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(2i-1\right){x}$ |
| 83200.2-j1 |
83200.2-j |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.2 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{16} \cdot 5^{8} \cdot 13 \) |
$3.03528$ |
$(a+1), (-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.743253812$ |
$1.513956085$ |
4.501014528 |
\( \frac{116352}{325} a + \frac{263936}{325} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 16 i\) , \( 20 i - 16\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+16i{x}+20i-16$ |
*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.
