| 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-a1 |
2600.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2600.4 |
\( 2^{3} \cdot 5^{2} \cdot 13 \) |
\( 2^{8} \cdot 5^{3} \cdot 13 \) |
$1.27618$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.197674831$ |
1.598837415 |
\( -\frac{43261952}{325} a - \frac{129542144}{325} \) |
\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 14 i - 2\) , \( 20 i + 5\bigr] \) |
${y}^2={x}^{3}+\left(i+1\right){x}^{2}+\left(14i-2\right){x}+20i+5$ |
| 26000.4-d1 |
26000.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{9} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.568858194$ |
$1.430043658$ |
3.253968216 |
\( -\frac{43261952}{325} a - \frac{129542144}{325} \) |
\( \bigl[0\) , \( i\) , \( 0\) , \( -32 i + 59\) , \( 177 i + 155\bigr] \) |
${y}^2={x}^{3}+i{x}^{2}+\left(-32i+59\right){x}+177i+155$ |
| 26000.6-a1 |
26000.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.6 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{9} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.430043658$ |
1.430043658 |
\( -\frac{43261952}{325} a - \frac{129542144}{325} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -48 i - 47\) , \( -182 i - 64\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(-48i-47\right){x}-182i-64$ |
| 65000.6-f1 |
65000.6-f |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65000.6 |
\( 2^{3} \cdot 5^{4} \cdot 13 \) |
\( 2^{8} \cdot 5^{15} \cdot 13 \) |
$2.85362$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.639534966$ |
2.558139865 |
\( -\frac{43261952}{325} a - \frac{129542144}{325} \) |
\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 334 i - 50\) , \( 1924 i + 1401\bigr] \) |
${y}^2={x}^{3}+\left(-i-1\right){x}^{2}+\left(334i-50\right){x}+1924i+1401$ |
| 67600.6-g1 |
67600.6-g |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{3} \cdot 13^{7} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.371256731$ |
$0.886875428$ |
4.864535603 |
\( -\frac{43261952}{325} a - \frac{129542144}{325} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 42 i - 170\) , \( -394 i + 877\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(42i-170\right){x}-394i+877$ |
| 83200.4-d1 |
83200.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.4 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{8} \cdot 5^{3} \cdot 13 \) |
$3.03528$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.257124254$ |
$3.197674831$ |
4.019874589 |
\( -\frac{43261952}{325} a - \frac{129542144}{325} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -14 i + 2\) , \( -5 i + 20\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-14i+2\right){x}-5i+20$ |
*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.
