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-d1 |
3872.14-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.14 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{48} \cdot 11^{3} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.478347664$ |
2.892774765 |
\( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) |
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 30 a + 86\) , \( -500 a - 580\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(30a+86\right){x}-500a-580$ |
3872.5-d1 |
3872.5-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
3872.5 |
\( 2^{5} \cdot 11^{2} \) |
\( 2^{48} \cdot 11^{3} \) |
$1.86497$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.478347664$ |
2.892774765 |
\( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -48 a - 65\) , \( 352 a - 1185\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-48a-65\right){x}+352a-1185$ |
5324.6-d1 |
5324.6-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.6 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{36} \cdot 11^{9} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{9} \) |
$0.245619348$ |
$0.288454494$ |
3.427684460 |
\( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) |
\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -48 a - 272\) , \( -3251 a + 4009\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-48a-272\right){x}-3251a+4009$ |
5324.7-c1 |
5324.7-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.7 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{36} \cdot 11^{9} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.964954788$ |
$0.288454494$ |
3.427684460 |
\( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) |
\( \bigl[1\) , \( 1\) , \( a\) , \( 157 a + 140\) , \( 3795 a - 654\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(157a+140\right){x}+3795a-654$ |
15488.20-c2 |
15488.20-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.20 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{54} \cdot 11^{3} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.338242877$ |
1.022750326 |
\( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -148 a - 29\) , \( -567 a - 2768\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-148a-29\right){x}-567a-2768$ |
15488.5-c2 |
15488.5-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
15488.5 |
\( 2^{7} \cdot 11^{2} \) |
\( 2^{54} \cdot 11^{3} \) |
$2.63746$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.338242877$ |
1.022750326 |
\( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) |
\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -19 a + 228\) , \( -129 a - 3075\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-19a+228\right){x}-129a-3075$ |
23716.5-e2 |
23716.5-e |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
23716.5 |
\( 2^{2} \cdot 7^{2} \cdot 11^{2} \) |
\( 2^{36} \cdot 7^{6} \cdot 11^{3} \) |
$2.93392$ |
$(a), (-a+1), (-2a+1), (-2a+3), (2a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.361596845$ |
1.093366089 |
\( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) |
\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 128 a - 155\) , \( 293 a + 2482\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(128a-155\right){x}+293a+2482$ |
*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.