| 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-a2 |
2600.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2600.4 |
\( 2^{3} \cdot 5^{2} \cdot 13 \) |
\( 2^{8} \cdot 5^{9} \cdot 13 \) |
$1.27618$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.598837415$ |
1.598837415 |
\( \frac{329359844912}{5078125} a - \frac{470870678516}{5078125} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -24 i + 37\) , \( 75 i + 67\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(-24i+37\right){x}+75i+67$ |
| 26000.4-d2 |
26000.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{15} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.568858194$ |
$0.715021829$ |
3.253968216 |
\( \frac{329359844912}{5078125} a - \frac{470870678516}{5078125} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( -79 i - 204\) , \( 570 i + 1169\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(-79i-204\right){x}+570i+1169$ |
| 26000.6-a2 |
26000.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.6 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{15} \cdot 13 \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.715021829$ |
1.430043658 |
\( \frac{329359844912}{5078125} a - \frac{470870678516}{5078125} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 217 i - 17\) , \( -982 i - 803\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(217i-17\right){x}-982i-803$ |
| 65000.6-f2 |
65000.6-f |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65000.6 |
\( 2^{3} \cdot 5^{4} \cdot 13 \) |
\( 2^{8} \cdot 5^{21} \cdot 13 \) |
$2.85362$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.319767483$ |
2.558139865 |
\( \frac{329359844912}{5078125} a - \frac{470870678516}{5078125} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -583 i + 919\) , \( 9196 i + 10797\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-583i+919\right){x}+9196i+10797$ |
| 67600.6-g2 |
67600.6-g |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{9} \cdot 13^{7} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.371256731$ |
$0.443437714$ |
4.864535603 |
\( \frac{329359844912}{5078125} a - \frac{470870678516}{5078125} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( 323 i + 464\) , \( -3191 i + 3939\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(323i+464\right){x}-3191i+3939$ |
| 83200.4-d2 |
83200.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.4 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{20} \cdot 5^{9} \cdot 13 \) |
$3.03528$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.257124254$ |
$0.799418707$ |
4.019874589 |
\( \frac{329359844912}{5078125} a - \frac{470870678516}{5078125} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( -94 i + 147\) , \( -511 i - 683\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(-94i+147\right){x}-511i-683$ |
*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.
