| 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-a4 |
512.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{17} \) |
$1.47247$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$18.70900640$ |
1.350206235 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -556 a + 964\) , \( -10464 a + 18124\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-556a+964\right){x}-10464a+18124$ |
| 512.1-b4 |
512.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{17} \) |
$1.47247$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$2.592594401$ |
$5.952999858$ |
2.227664748 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -40 a + 70\) , \( 172 a - 298\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-40a+70\right){x}+172a-298$ |
| 512.1-g4 |
512.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{17} \) |
$1.47247$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.648148600$ |
$5.952999858$ |
2.227664748 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -556 a + 964\) , \( 10464 a - 18124\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-556a+964\right){x}+10464a-18124$ |
| 512.1-h4 |
512.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( - 2^{17} \) |
$1.47247$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$18.70900640$ |
1.350206235 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -40 a + 70\) , \( -172 a + 298\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-40a+70\right){x}-172a+298$ |
| 1024.1-c4 |
1024.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{23} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.55342183$ |
1.523255234 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -298 a + 517\) , \( 3807 a - 6594\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-298a+517\right){x}+3807a-6594$ |
| 1024.1-d4 |
1024.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{23} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.741115149$ |
$5.276710919$ |
2.652162765 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -22 a + 37\) , \( -89 a + 154\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-22a+37\right){x}-89a+154$ |
| 1024.1-q4 |
1024.1-q |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{23} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.276710919$ |
1.523255234 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -10 a - 11\) , \( -23 a - 38\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-10a-11\right){x}-23a-38$ |
| 1024.1-r4 |
1024.1-r |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( - 2^{23} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.741115149$ |
$10.55342183$ |
2.652162765 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -22 a + 37\) , \( 89 a - 154\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-22a+37\right){x}+89a-154$ |
| 4608.1-a4 |
4608.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( - 2^{17} \cdot 3^{6} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$8.616832848$ |
2.487465382 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -120 a + 207\) , \( 1014 a - 1756\bigr] \) |
${y}^2={x}^{3}+\left(-120a+207\right){x}+1014a-1756$ |
| 4608.1-f4 |
4608.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( - 2^{17} \cdot 3^{6} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1.442267495$ |
$8.616832848$ |
3.587590466 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1668 a + 2889\) , \( 52704 a - 91286\bigr] \) |
${y}^2={x}^{3}+\left(-1668a+2889\right){x}+52704a-91286$ |
| 4608.1-bb4 |
4608.1-bb |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( - 2^{17} \cdot 3^{6} \) |
$2.55039$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$4$ |
\( 2 \) |
$1$ |
$4.308416424$ |
2.487465382 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1668 a + 2889\) , \( -52704 a + 91286\bigr] \) |
${y}^2={x}^{3}+\left(-1668a+2889\right){x}-52704a+91286$ |
| 4608.1-be4 |
4608.1-be |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
4608.1 |
\( 2^{9} \cdot 3^{2} \) |
\( - 2^{17} \cdot 3^{6} \) |
$2.55039$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1.442267495$ |
$4.308416424$ |
3.587590466 |
\( 2002968 a + 3470040 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -120 a + 207\) , \( -1014 a + 1756\bigr] \) |
${y}^2={x}^{3}+\left(-120a+207\right){x}-1014a+1756$ |
*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.
