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 |
882.2-a1 |
882.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
882.2 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{2} \) |
$1.37737$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.570759829$ |
$2.740367332$ |
2.211959540 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-4{x}+5$ |
7056.2-f1 |
7056.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7056.2 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{28} \cdot 3^{4} \cdot 7^{2} \) |
$2.31645$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.370183666$ |
3.875464647 |
\( -\frac{7189057}{16128} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -15\) , \( 58\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-15{x}+58$ |
7938.3-a1 |
7938.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2^{16} \cdot 3^{16} \cdot 7^{2} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.913455777$ |
1.291821549 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( -176\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}-36{x}-176$ |
43218.2-f1 |
43218.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
43218.2 |
\( 2 \cdot 3^{2} \cdot 7^{4} \) |
\( 2^{16} \cdot 3^{4} \cdot 7^{14} \) |
$3.64418$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.391481047$ |
4.429102453 |
\( -\frac{7189057}{16128} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -197\) , \( -2367\bigr] \) |
${y}^2+{x}{y}={x}^{3}-197{x}-2367$ |
*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.