| 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 |
| 2601.5-a1 |
2601.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{10} \cdot 17^{4} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
|
|
$1$ |
\( 3^{3} \) |
$0.018964757$ |
$2.164363860$ |
1.567315135 |
\( \frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) |
\( \bigl[0\) , \( a\) , \( a + 1\) , \( 3 a - 5\) , \( -2 a + 10\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(3a-5\right){x}-2a+10$ |
| 23409.8-j1 |
23409.8-j |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{22} \cdot 17^{4} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$0.721454620$ |
4.081163634 |
\( \frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) |
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 27 a - 39\) , \( -a - 317\bigr] \) |
${y}^2+\left(a+1\right){y}={x}^{3}+\left(27a-39\right){x}-a-317$ |
| 41616.5-o1 |
41616.5-o |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.5 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{12} \cdot 3^{10} \cdot 17^{4} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 3 \) |
$1.187019453$ |
$1.082181930$ |
5.449973205 |
\( \frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a - 18\) , \( 6 a + 102\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(12a-18\right){x}+6a+102$ |
| 44217.6-e1 |
44217.6-e |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.6 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{10} \cdot 17^{10} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \cdot 3^{2} \) |
$1.186590409$ |
$0.524935341$ |
15.85601871 |
\( \frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 55 a + 68\) , \( -429 a - 505\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+\left(55a+68\right){x}-429a-505$ |
| 44217.7-d1 |
44217.7-d |
$1$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{10} \cdot 17^{10} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$0.524935341$ |
1.484741359 |
\( \frac{14811123712}{96702579} a + \frac{26737709056}{96702579} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -49 a - 76\) , \( 462 a - 505\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}+\left(-49a-76\right){x}+462a-505$ |
*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.
