| 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-a5 |
882.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
882.2 |
\( 2 \cdot 3^{2} \cdot 7^{2} \) |
\( 2 \cdot 3^{40} \cdot 7^{2} \) |
$1.37737$ |
$(a), (-a-1), (a-1), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$9.132157269$ |
$0.171272958$ |
2.211959540 |
\( -\frac{4649899211841477010577}{25942282643925774} a + \frac{175460189537451816680}{1853020188851841} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -595 a + 4306\) , \( 75404 a + 34009\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-595a+4306\right){x}+75404a+34009$ |
| 7056.2-f5 |
7056.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7056.2 |
\( 2^{4} \cdot 3^{2} \cdot 7^{2} \) |
\( 2^{13} \cdot 3^{40} \cdot 7^{2} \) |
$2.31645$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{10} \) |
$1$ |
$0.085636479$ |
3.875464647 |
\( -\frac{4649899211841477010577}{25942282643925774} a + \frac{175460189537451816680}{1853020188851841} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -2380 a + 17225\) , \( 605612 a + 254850\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-2380a+17225\right){x}+605612a+254850$ |
| 7938.3-a5 |
7938.3-a |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
7938.3 |
\( 2 \cdot 3^{4} \cdot 7^{2} \) |
\( 2 \cdot 3^{52} \cdot 7^{2} \) |
$2.38568$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$16$ |
\( 2^{3} \) |
$1$ |
$0.057090986$ |
1.291821549 |
\( -\frac{4649899211841477010577}{25942282643925774} a + \frac{175460189537451816680}{1853020188851841} \) |
\( \bigl[1\) , \( -1\) , \( 0\) , \( -5355 a + 38754\) , \( -2041263 a - 879494\bigr] \) |
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-5355a+38754\right){x}-2041263a-879494$ |
| 43218.2-f5 |
43218.2-f |
$8$ |
$16$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
43218.2 |
\( 2 \cdot 3^{2} \cdot 7^{4} \) |
\( 2 \cdot 3^{40} \cdot 7^{14} \) |
$3.64418$ |
$(a), (-a-1), (a-1), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{10} \) |
$1$ |
$0.024467565$ |
4.429102453 |
\( -\frac{4649899211841477010577}{25942282643925774} a + \frac{175460189537451816680}{1853020188851841} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -29155 a + 210993\) , \( -25951037 a - 11032169\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-29155a+210993\right){x}-25951037a-11032169$ |
*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.
