| 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 |
| 2080.2-b1 |
2080.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2080.2 |
\( 2^{5} \cdot 5 \cdot 13 \) |
\( 2^{6} \cdot 5 \cdot 13 \) |
$1.20694$ |
$(a+1), (-a-2), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$3.254761685$ |
1.627380842 |
\( \frac{965386184}{65} a - \frac{555859168}{65} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 19 i + 11\) , \( 8 i - 38\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(19i+11\right){x}+8i-38$ |
| 10400.2-a1 |
10400.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
10400.2 |
\( 2^{5} \cdot 5^{2} \cdot 13 \) |
\( 2^{6} \cdot 5^{7} \cdot 13 \) |
$1.80479$ |
$(a+1), (-a-2), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.765680601$ |
$1.455573675$ |
2.570078203 |
\( \frac{965386184}{65} a - \frac{555859168}{65} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -100 i + 42\) , \( -22 i + 459\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-100i+42\right){x}-22i+459$ |
| 16640.2-b1 |
16640.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
16640.2 |
\( 2^{8} \cdot 5 \cdot 13 \) |
\( 2^{18} \cdot 5 \cdot 13 \) |
$2.02982$ |
$(a+1), (-a-2), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.627380842$ |
1.627380842 |
\( \frac{965386184}{65} a - \frac{555859168}{65} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 74 i + 43\) , \( -11 i - 347\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(74i+43\right){x}-11i-347$ |
| 27040.3-b1 |
27040.3-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
27040.3 |
\( 2^{5} \cdot 5 \cdot 13^{2} \) |
\( 2^{6} \cdot 5 \cdot 13^{7} \) |
$2.29177$ |
$(a+1), (-a-2), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.902708472$ |
1.805416945 |
\( \frac{965386184}{65} a - \frac{555859168}{65} \) |
\( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 222 i - 170\) , \( 1872 i - 369\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-i+1\right){x}^{2}+\left(222i-170\right){x}+1872i-369$ |
| 52000.6-a1 |
52000.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
52000.6 |
\( 2^{5} \cdot 5^{3} \cdot 13 \) |
\( 2^{6} \cdot 5^{7} \cdot 13 \) |
$2.69879$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.592726322$ |
$1.455573675$ |
3.451027329 |
\( \frac{965386184}{65} a - \frac{555859168}{65} \) |
\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -14 i - 107\) , \( 95 i + 421\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-i{x}^{2}+\left(-14i-107\right){x}+95i+421$ |
| 66560.2-h1 |
66560.2-h |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.2 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{24} \cdot 5 \cdot 13 \) |
$2.87059$ |
$(a+1), (-a-2), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$1.150732029$ |
2.301464058 |
\( \frac{965386184}{65} a - \frac{555859168}{65} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 86 i - 149\) , \( 586 i - 567\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(86i-149\right){x}+586i-567$ |
| 66560.2-l1 |
66560.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
66560.2 |
\( 2^{10} \cdot 5 \cdot 13 \) |
\( 2^{24} \cdot 5 \cdot 13 \) |
$2.87059$ |
$(a+1), (-a-2), (2a+3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.506615105$ |
$1.150732029$ |
5.768884573 |
\( \frac{965386184}{65} a - \frac{555859168}{65} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -86 i + 149\) , \( -567 i - 586\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-86i+149\right){x}-567i-586$ |
| 83200.2-l1 |
83200.2-l |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.2 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{18} \cdot 5^{7} \cdot 13 \) |
$3.03528$ |
$(a+1), (-a-2), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.727786837$ |
1.455573675 |
\( \frac{965386184}{65} a - \frac{555859168}{65} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -396 i + 170\) , \( -742 i + 3444\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(-396i+170\right){x}-742i+3444$ |
*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.
