| 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 |
| 512.1-a3 |
512.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.47247$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$9.354503203$ |
1.350206235 |
\( 23328 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 6 a - 11\) , \( 15 a - 26\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(6a-11\right){x}+15a-26$ |
| 512.1-b3 |
512.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.47247$ |
$(a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.648148600$ |
$23.81199943$ |
2.227664748 |
\( 23328 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -6 a - 11\) , \( 15 a + 26\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-6a-11\right){x}+15a+26$ |
| 512.1-g3 |
512.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.47247$ |
$(a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.648148600$ |
$23.81199943$ |
2.227664748 |
\( 23328 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 6 a - 11\) , \( -15 a + 26\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(6a-11\right){x}-15a+26$ |
| 512.1-h3 |
512.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.47247$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$9.354503203$ |
1.350206235 |
\( 23328 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -6 a - 11\) , \( -15 a - 26\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-6a-11\right){x}-15a-26$ |
| 1024.1-c3 |
1024.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$21.10684367$ |
1.523255234 |
\( 23328 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 12 a - 20\) , \( -22 a + 38\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(12a-20\right){x}-22a+38$ |
| 1024.1-d3 |
1024.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.435278787$ |
$21.10684367$ |
2.652162765 |
\( 23328 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -2\) , \( 2 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-2{x}+2a$ |
| 1024.1-q3 |
1024.1-q |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$21.10684367$ |
1.523255234 |
\( 23328 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -12 a - 20\) , \( 22 a + 38\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-12a-20\right){x}+22a+38$ |
| 1024.1-r3 |
1024.1-r |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.435278787$ |
$21.10684367$ |
2.652162765 |
\( 23328 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -2\) , \( -2 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-2{x}-2a$ |
| 4608.1-a3 |
4608.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.616832848$ |
2.487465382 |
\( 23328 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -18 a - 36\) , \( -60 a - 100\bigr] \) |
${y}^2={x}^{3}+\left(-18a-36\right){x}-60a-100$ |
| 4608.1-f3 |
4608.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.360566873$ |
$8.616832848$ |
3.587590466 |
\( 23328 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 18 a - 36\) , \( -60 a + 100\bigr] \) |
${y}^2={x}^{3}+\left(18a-36\right){x}-60a+100$ |
| 4608.1-bb3 |
4608.1-bb |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.616832848$ |
2.487465382 |
\( 23328 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 18 a - 36\) , \( 60 a - 100\bigr] \) |
${y}^2={x}^{3}+\left(18a-36\right){x}+60a-100$ |
| 4608.1-be3 |
4608.1-be |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{6} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.360566873$ |
$8.616832848$ |
3.587590466 |
\( 23328 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -18 a - 36\) , \( 60 a + 100\bigr] \) |
${y}^2={x}^{3}+\left(-18a-36\right){x}+60a+100$ |
*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.
