| 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 |
| 392.1-a1 |
392.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$1.12462$ |
$(a), (7)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1.069108576$ |
$8.032591436$ |
1.518107418 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 2\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+2{x}$ |
| 784.1-b1 |
784.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$1.33740$ |
$(a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.696738583$ |
$8.032591436$ |
1.978702696 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+{x}$ |
| 19208.1-d1 |
19208.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
19208.1 |
\( 2^{3} \cdot 7^{4} \) |
\( 2^{4} \cdot 7^{14} \) |
$2.97546$ |
$(a), (7)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$3.657265035$ |
$1.147513062$ |
5.935114063 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 14\) , \( 80\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+14{x}+80$ |
| 31752.3-i1 |
31752.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
31752.3 |
\( 2^{3} \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{4} \cdot 3^{12} \cdot 7^{2} \) |
$3.37385$ |
$(a), (-a-1), (a-1), (7)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.677530478$ |
3.786599916 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 4\) , \( 6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+4{x}+6$ |
| 38416.1-f1 |
38416.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
38416.1 |
\( 2^{4} \cdot 7^{4} \) |
\( 2^{4} \cdot 7^{14} \) |
$3.53844$ |
$(a), (7)$ |
$0$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.147513062$ |
3.245657071 |
\( \frac{432}{7} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 13\) , \( -92\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+13{x}-92$ |
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*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.
