| 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-a4 |
2600.4-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
2600.4 |
\( 2^{3} \cdot 5^{2} \cdot 13 \) |
\( 2^{8} \cdot 5^{6} \cdot 13^{4} \) |
$1.27618$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$1.598837415$ |
1.598837415 |
\( \frac{17012483856}{17850625} a + \frac{53748185108}{17850625} \) |
\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( 16 i - 13\) , \( 21 i - 3\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(-i-1\right){x}^{2}+\left(16i-13\right){x}+21i-3$ |
| 26000.4-d4 |
26000.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.4 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{12} \cdot 13^{4} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$0.568858194$ |
$0.715021829$ |
3.253968216 |
\( \frac{17012483856}{17850625} a + \frac{53748185108}{17850625} \) |
\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( i + 106\) , \( 346 i - 99\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}+\left(i-1\right){x}^{2}+\left(i+106\right){x}+346i-99$ |
| 26000.6-a4 |
26000.6-a |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
26000.6 |
\( 2^{4} \cdot 5^{3} \cdot 13 \) |
\( 2^{8} \cdot 5^{12} \cdot 13^{4} \) |
$2.26940$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.715021829$ |
1.430043658 |
\( \frac{17012483856}{17850625} a + \frac{53748185108}{17850625} \) |
\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -103 i - 27\) , \( -258 i + 179\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+\left(-103i-27\right){x}-258i+179$ |
| 65000.6-f4 |
65000.6-f |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
65000.6 |
\( 2^{3} \cdot 5^{4} \cdot 13 \) |
\( 2^{8} \cdot 5^{18} \cdot 13^{4} \) |
$2.85362$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.319767483$ |
2.558139865 |
\( \frac{17012483856}{17850625} a + \frac{53748185108}{17850625} \) |
\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( 417 i - 331\) , \( 3196 i - 1453\bigr] \) |
${y}^2+\left(i+1\right){x}{y}={x}^{3}+{x}^{2}+\left(417i-331\right){x}+3196i-1453$ |
| 67600.6-g4 |
67600.6-g |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
67600.6 |
\( 2^{4} \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 5^{6} \cdot 13^{10} \) |
$2.88174$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.371256731$ |
$0.443437714$ |
4.864535603 |
\( \frac{17012483856}{17850625} a + \frac{53748185108}{17850625} \) |
\( \bigl[i + 1\) , \( -1\) , \( i + 1\) , \( -77 i - 266\) , \( 673 i + 1155\bigr] \) |
${y}^2+\left(i+1\right){x}{y}+\left(i+1\right){y}={x}^{3}-{x}^{2}+\left(-77i-266\right){x}+673i+1155$ |
| 83200.4-d4 |
83200.4-d |
$6$ |
$8$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
83200.4 |
\( 2^{8} \cdot 5^{2} \cdot 13 \) |
\( 2^{20} \cdot 5^{6} \cdot 13^{4} \) |
$3.03528$ |
$(a+1), (-a-2), (2a+1), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.257124254$ |
$0.799418707$ |
4.019874589 |
\( \frac{17012483856}{17850625} a + \frac{53748185108}{17850625} \) |
\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 66 i - 53\) , \( -239 i + 77\bigr] \) |
${y}^2={x}^{3}+\left(i-1\right){x}^{2}+\left(66i-53\right){x}-239i+77$ |
*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.
