| 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-e2 |
2601.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{8} \cdot 17^{8} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.886283983$ |
1.880092244 |
\( -\frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -67 a + 7\) , \( 158 a - 254\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-67a+7\right){x}+158a-254$ |
| 23409.8-e2 |
23409.8-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{20} \cdot 17^{8} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.627781647$ |
$0.295427994$ |
3.147433083 |
\( -\frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -605 a + 61\) , \( -4808 a + 8130\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-605a+61\right){x}-4808a+8130$ |
| 41616.5-l2 |
41616.5-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.5 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{12} \cdot 3^{8} \cdot 17^{8} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.443141991$ |
1.253394829 |
\( -\frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -270 a + 29\) , \( 1533 a - 2059\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-270a+29\right){x}+1533a-2059$ |
| 44217.6-a2 |
44217.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.6 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{8} \cdot 17^{14} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.214955439$ |
0.303992898 |
\( -\frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -151 a - 1607\) , \( 2693 a + 25042\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-151a-1607\right){x}+2693a+25042$ |
| 44217.7-b2 |
44217.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{8} \cdot 17^{14} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$1$ |
$0.214955439$ |
2.735936085 |
\( -\frac{147770521717808}{17596287801} a - \frac{136210703475223}{17596287801} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 16 a + 1621\) , \( -18381 a - 544\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(16a+1621\right){x}-18381a-544$ |
*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.
