| 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 |
| 3872.14-d5 |
3872.14-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.14 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{9} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.239173832$ |
2.892774765 |
\( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 2138 a + 2479\) , \( 46031 a - 123975\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2138a+2479\right){x}+46031a-123975$ |
| 3872.5-d5 |
3872.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{24} \cdot 11^{9} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.239173832$ |
2.892774765 |
\( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -2738 a - 1366\) , \( 86180 a - 19585\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-2738a-1366\right){x}+86180a-19585$ |
| 5324.6-d5 |
5324.6-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.6 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{12} \cdot 11^{15} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1.964954788$ |
$0.144227247$ |
3.427684460 |
\( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) |
\( \bigl[1\) , \( a\) , \( 0\) , \( -4707 a - 8462\) , \( -291111 a - 234502\bigr] \) |
${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-4707a-8462\right){x}-291111a-234502$ |
| 5324.7-c5 |
5324.7-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.7 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{12} \cdot 11^{15} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.982477394$ |
$0.144227247$ |
3.427684460 |
\( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) |
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 8297 a + 1789\) , \( 17536 a + 527872\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(8297a+1789\right){x}+17536a+527872$ |
| 15488.20-c6 |
15488.20-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{30} \cdot 11^{9} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.169121438$ |
1.022750326 |
\( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -6757 a + 1799\) , \( 217839 a - 268149\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-6757a+1799\right){x}+217839a-268149$ |
| 15488.5-c6 |
15488.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.5 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{30} \cdot 11^{9} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.169121438$ |
1.022750326 |
\( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) |
\( \bigl[a\) , \( -a\) , \( 0\) , \( 1372 a + 8207\) , \( 237584 a - 219739\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(1372a+8207\right){x}+237584a-219739$ |
| 23716.5-e6 |
23716.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{12} \cdot 7^{6} \cdot 11^{9} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.180798422$ |
1.093366089 |
\( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) |
\( \bigl[1\) , \( a + 1\) , \( a\) , \( 4189 a - 7784\) , \( -188092 a + 197516\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4189a-7784\right){x}-188092a+197516$ |
*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.
