| 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-e4 |
2601.5-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
2601.5 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{4} \cdot 17^{7} \) |
$1.80496$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$1.772567966$ |
1.880092244 |
\( \frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -7 a + 12\) , \( 14 a + 23\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-7a+12\right){x}+14a+23$ |
| 23409.8-e4 |
23409.8-e |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
23409.8 |
\( 3^{4} \cdot 17^{2} \) |
\( 3^{16} \cdot 17^{7} \) |
$3.12629$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \cdot 3 \) |
$0.313890823$ |
$0.590855988$ |
3.147433083 |
\( \frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -65 a + 106\) , \( -335 a - 384\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-65a+106\right){x}-335a-384$ |
| 41616.5-l4 |
41616.5-l |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
41616.5 |
\( 2^{4} \cdot 3^{2} \cdot 17^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 17^{7} \) |
$3.60993$ |
$(a), (-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.886283983$ |
1.253394829 |
\( \frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) |
\( \bigl[a\) , \( a - 1\) , \( a\) , \( -30 a + 49\) , \( 141 a + 137\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-30a+49\right){x}+141a+137$ |
| 44217.6-a4 |
44217.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.6 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{4} \cdot 17^{13} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$0.429910879$ |
0.303992898 |
\( \frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -151 a - 162\) , \( -1353 a + 188\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-151a-162\right){x}-1353a+188$ |
| 44217.7-b4 |
44217.7-b |
$4$ |
$4$ |
\(\Q(\sqrt{-2}) \) |
$2$ |
$[0, 1]$ |
44217.7 |
\( 3^{2} \cdot 17^{3} \) |
\( 3^{4} \cdot 17^{13} \) |
$3.66506$ |
$(-a-1), (a-1), (-2a+3), (2a+3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1$ |
$0.429910879$ |
2.735936085 |
\( \frac{3780522976}{2255067} a + \frac{417620747}{2255067} \) |
\( \bigl[1\) , \( 0\) , \( a\) , \( 136 a + 186\) , \( 60 a - 1825\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+\left(136a+186\right){x}+60a-1825$ |
*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.
