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 |
3528.2-a1 |
3528.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3528.2 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{8} \) |
$1.94790$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.390851865$ |
0.983480785 |
\( -\frac{2725888}{64827} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 52\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-7{x}+52$ |
3528.2-a2 |
3528.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3528.2 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{24} \cdot 7^{2} \) |
$1.94790$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.695425932$ |
0.983480785 |
\( \frac{6522128932}{3720087} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -97\) , \( 29\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-97{x}+29$ |
3528.2-a3 |
3528.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3528.2 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{4} \) |
$1.94790$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.390851865$ |
0.983480785 |
\( \frac{6940769488}{35721} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -62\) , \( -202\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-62{x}-202$ |
3528.2-a4 |
3528.2-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3528.2 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 7^{2} \) |
$1.94790$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$0.695425932$ |
0.983480785 |
\( \frac{7080974546692}{189} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -1007\) , \( -12487\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-1007{x}-12487$ |
3528.2-b1 |
3528.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3528.2 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{8} \) |
$1.94790$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.972356834$ |
2.789333785 |
\( \frac{11696828}{7203} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 12\) , \( -6\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+12{x}-6$ |
3528.2-b2 |
3528.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3528.2 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{4} \cdot 7^{4} \) |
$1.94790$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.944713669$ |
2.789333785 |
\( \frac{810448}{441} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -3\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-3{x}$ |
3528.2-b3 |
3528.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3528.2 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{2} \cdot 7^{2} \) |
$1.94790$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.944713669$ |
2.789333785 |
\( \frac{2725888}{21} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -10\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-7{x}-10$ |
3528.2-b4 |
3528.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
3528.2 |
\( 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{8} \cdot 7^{2} \) |
$1.94790$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.972356834$ |
2.789333785 |
\( \frac{381775972}{567} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -38\) , \( -84\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-38{x}-84$ |
*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.