| 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 |
| 4032.4-a1 |
4032.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.4 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{2} \cdot 7^{8} \) |
$1.88394$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.986178417$ |
1.490961623 |
\( \frac{11696828}{7203} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 48\) , \( 48\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+48{x}+48$ |
| 4032.4-a2 |
4032.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.4 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{4} \) |
$1.88394$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.972356834$ |
1.490961623 |
\( \frac{810448}{441} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -12\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-12{x}$ |
| 4032.4-a3 |
4032.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.4 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
$1.88394$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$3.944713669$ |
1.490961623 |
\( \frac{2725888}{21} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -10\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-7{x}-10$ |
| 4032.4-a4 |
4032.4-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.4 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{8} \cdot 7^{2} \) |
$1.88394$ |
$(a), (-a+1), (-2a+1), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.986178417$ |
1.490961623 |
\( \frac{381775972}{567} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -152\) , \( 672\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-152{x}+672$ |
| 4032.4-b1 |
4032.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.4 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{8} \) |
$1.88394$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.249128130$ |
$1.390851865$ |
3.143155507 |
\( -\frac{2725888}{64827} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 52\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-7{x}+52$ |
| 4032.4-b2 |
4032.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.4 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{24} \cdot 7^{2} \) |
$1.88394$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.996512522$ |
$0.347712966$ |
3.143155507 |
\( \frac{6522128932}{3720087} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -392\) , \( -228\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-392{x}-228$ |
| 4032.4-b3 |
4032.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.4 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{16} \cdot 3^{12} \cdot 7^{4} \) |
$1.88394$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3 \) |
$0.498256261$ |
$0.695425932$ |
3.143155507 |
\( \frac{6940769488}{35721} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -252\) , \( 1620\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-252{x}+1620$ |
| 4032.4-b4 |
4032.4-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
4032.4 |
\( 2^{6} \cdot 3^{2} \cdot 7 \) |
\( 2^{20} \cdot 3^{6} \cdot 7^{2} \) |
$1.88394$ |
$(a), (-a+1), (-2a+1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3 \) |
$0.996512522$ |
$0.347712966$ |
3.143155507 |
\( \frac{7080974546692}{189} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4032\) , \( 99900\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-4032{x}+99900$ |
*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.
