| 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-e3 |
2601.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{4} \cdot 17^{13} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$0.443141991$ |
1.880092244 |
\( -\frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -7 a - 158\) , \( 2 a - 1661\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-7a-158\right){x}+2a-1661$ |
| 23409.8-e3 |
23409.8-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{16} \cdot 17^{13} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3 \) |
$1.255563294$ |
$0.147713997$ |
3.147433083 |
\( -\frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -65 a - 1424\) , \( -1541 a + 43554\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-65a-1424\right){x}-1541a+43554$ |
| 41616.5-l3 |
41616.5-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.5 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 17^{13} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{3} \) |
$1$ |
$0.221570995$ |
1.253394829 |
\( -\frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -30 a - 631\) , \( 45 a - 12655\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-30a-631\right){x}+45a-12655$ |
| 44217.6-a3 |
44217.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.6 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{4} \cdot 17^{19} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$0.107477719$ |
0.303992898 |
\( -\frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 1889 a - 332\) , \( 61139 a + 75226\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(1889a-332\right){x}+61139a+75226$ |
| 44217.7-b3 |
44217.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{4} \cdot 17^{19} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \cdot 3^{2} \) |
$1$ |
$0.107477719$ |
2.735936085 |
\( -\frac{1695948356939509768}{15730800405203547} a - \frac{7330062339265374821}{15730800405203547} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( -1904 a + 16\) , \( -63222 a + 70787\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(-1904a+16\right){x}-63222a+70787$ |
*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.
