| 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 |
| 2600.4-a5 |
2600.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2600.4 |
\( 2^{3} \cdot 5^{2} \cdot 13 \) |
\( 2^{10} \cdot 5^{3} \cdot 13^{8} \) |
$1.27618$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.799418707$ |
1.598837415 |
\( -\frac{263319363133844}{20393268025} a + \frac{443594369492878}{20393268025} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( 116 i - 63\) , \( -599 i + 7\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(116i-63\right){x}-599i+7$ |
| 26000.4-d5 |
26000.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{10} \cdot 5^{9} \cdot 13^{8} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.284429097$ |
$0.357510914$ |
3.253968216 |
\( -\frac{263319363133844}{20393268025} a + \frac{443594369492878}{20393268025} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( -99 i + 656\) , \( -5844 i - 1679\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-99i+656\right){x}-5844i-1679$ |
| 26000.6-a5 |
26000.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.6 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{10} \cdot 5^{9} \cdot 13^{8} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.357510914$ |
1.430043658 |
\( -\frac{263319363133844}{20393268025} a + \frac{443594369492878}{20393268025} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -603 i - 277\) , \( 6292 i - 671\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-603i-277\right){x}+6292i-671$ |
| 65000.6-f5 |
65000.6-f |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65000.6 |
\( 2^{3} \cdot 5^{4} \cdot 13 \) |
\( 2^{10} \cdot 5^{15} \cdot 13^{8} \) |
$2.85362$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.159883741$ |
2.558139865 |
\( -\frac{263319363133844}{20393268025} a + \frac{443594369492878}{20393268025} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 2917 i - 1581\) , \( -70554 i - 5203\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(2917i-1581\right){x}-70554i-5203$ |
| 67600.6-g5 |
67600.6-g |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{10} \cdot 5^{3} \cdot 13^{14} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.742513462$ |
$0.221718857$ |
4.864535603 |
\( -\frac{263319363133844}{20393268025} a + \frac{443594369492878}{20393268025} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -177 i - 1716\) , \( -3817 i - 25925\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-177i-1716\right){x}-3817i-25925$ |
| 83200.4-d5 |
83200.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.4 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{22} \cdot 5^{3} \cdot 13^{8} \) |
$3.03528$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.514248509$ |
$0.399709353$ |
4.019874589 |
\( -\frac{263319363133844}{20393268025} a + \frac{443594369492878}{20393268025} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 466 i - 253\) , \( 4321 i + 197\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(466i-253\right){x}+4321i+197$ |
*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.
