| 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-d2 |
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 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.478347664$ |
2.892774765 |
\( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 46 a - 113\) , \( -353 a - 833\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(46a-113\right){x}-353a-833$ |
| 3872.5-d2 |
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 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{7} \) |
$1$ |
$0.478347664$ |
2.892774765 |
\( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) |
\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -30 a + 117\) , \( 617 a - 1138\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-30a+117\right){x}+617a-1138$ |
| 5324.6-d2 |
5324.6-d |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.6 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{36} \cdot 11^{9} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.964954788$ |
$0.288454494$ |
3.427684460 |
\( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) |
\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -158 a + 297\) , \( -3796 a + 3141\bigr] \) |
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-158a+297\right){x}-3796a+3141$ |
| 5324.7-c2 |
5324.7-c |
$6$ |
$8$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
5324.7 |
\( 2^{2} \cdot 11^{3} \) |
\( 2^{36} \cdot 11^{9} \) |
$2.01952$ |
$(a), (-a+1), (-2a+3), (2a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{9} \) |
$0.245619348$ |
$0.288454494$ |
3.427684460 |
\( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) |
\( \bigl[1\) , \( a\) , \( 1\) , \( 48 a - 320\) , \( 3251 a + 758\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(48a-320\right){x}+3251a+758$ |
| 15488.20-c1 |
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 |
\( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) |
\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 17 a + 209\) , \( 128 a - 3204\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(17a+209\right){x}+128a-3204$ |
| 15488.5-c1 |
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 |
\( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 146 a - 175\) , \( 566 a - 3334\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(146a-175\right){x}+566a-3334$ |
| 23716.5-e1 |
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 |
\( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) |
\( \bigl[1\) , \( a - 1\) , \( a\) , \( -129 a - 26\) , \( -294 a + 2776\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-129a-26\right){x}-294a+2776$ |
*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.
