| 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-b2 |
8320.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
8320.2 |
\( 2^{7} \cdot 5 \cdot 13 \) |
\( 2^{14} \cdot 5 \cdot 13^{2} \) |
$1.70687$ |
$(a+1), (-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.371825182$ |
$3.385308722$ |
2.517486070 |
\( -\frac{916768}{845} a + \frac{2571776}{845} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( 2 i + 4\) , \( 4 i - 2\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(2i+4\right){x}+4i-2$ |
| 16640.2-f2 |
16640.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16640.2 |
\( 2^{8} \cdot 5 \cdot 13 \) |
\( 2^{14} \cdot 5 \cdot 13^{2} \) |
$2.02982$ |
$(a+1), (-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.492021894$ |
$3.385308722$ |
3.331292019 |
\( -\frac{916768}{845} a + \frac{2571776}{845} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2 i - 4\) , \( -2 i - 4\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-2i-4\right){x}-2i-4$ |
| 41600.2-d2 |
41600.2-d |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
41600.2 |
\( 2^{7} \cdot 5^{2} \cdot 13 \) |
\( 2^{14} \cdot 5^{7} \cdot 13^{2} \) |
$2.55236$ |
$(a+1), (-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.665617626$ |
$1.513956085$ |
4.030863424 |
\( -\frac{916768}{845} a + \frac{2571776}{845} \) |
\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -24 i - 5\) , \( 25 i - 19\bigr] \) |
${y}^2={x}^{3}+\left(-i+1\right){x}^{2}+\left(-24i-5\right){x}+25i-19$ |
| 66560.2-f2 |
66560.2-f |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.2 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{20} \cdot 5 \cdot 13^{2} \) |
$2.87059$ |
$(a+1), (-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.443922595$ |
$2.393774754$ |
4.250602806 |
\( -\frac{916768}{845} a + \frac{2571776}{845} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 8 i - 4\) , \( -12 i - 4\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(8i-4\right){x}-12i-4$ |
| 66560.2-p2 |
66560.2-p |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.2 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{20} \cdot 5 \cdot 13^{2} \) |
$2.87059$ |
$(a+1), (-a-2), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.393774754$ |
2.393774754 |
\( -\frac{916768}{845} a + \frac{2571776}{845} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( -8 i + 4\) , \( 4 i - 12\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(-8i+4\right){x}+4i-12$ |
| 83200.2-j2 |
83200.2-j |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.2 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{14} \cdot 5^{7} \cdot 13^{2} \) |
$3.03528$ |
$(a+1), (-a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.371626906$ |
$1.513956085$ |
4.501014528 |
\( -\frac{916768}{845} a + \frac{2571776}{845} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 24 i + 5\) , \( 19 i + 25\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(24i+5\right){x}+19i+25$ |
*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.
