| 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-a1 |
512.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -2002968 a + 3470040 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 3064 a - 5306\) , \( -119716 a + 207354\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(3064a-5306\right){x}-119716a+207354$ |
| 512.1-b1 |
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 |
$1$ |
\( 2^{2} \) |
$0.648148600$ |
$5.952999858$ |
2.227664748 |
\( -2002968 a + 3470040 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 220 a - 380\) , \( 2464 a - 4268\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(220a-380\right){x}+2464a-4268$ |
| 512.1-g1 |
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 |
$1$ |
\( 1 \) |
$2.592594401$ |
$5.952999858$ |
2.227664748 |
\( -2002968 a + 3470040 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 3064 a - 5306\) , \( 119716 a - 207354\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(3064a-5306\right){x}+119716a-207354$ |
| 512.1-h1 |
512.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -2002968 a + 3470040 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 220 a - 380\) , \( -2464 a + 4268\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(220a-380\right){x}-2464a+4268$ |
| 1024.1-c1 |
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 |
$1$ |
\( 2^{2} \) |
$1$ |
$5.276710919$ |
1.523255234 |
\( -2002968 a + 3470040 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 1642 a - 2843\) , \( 48607 a - 84190\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(1642a-2843\right){x}+48607a-84190$ |
| 1024.1-d1 |
1024.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -2002968 a + 3470040 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 118 a - 203\) , \( -849 a + 1470\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(118a-203\right){x}-849a+1470$ |
| 1024.1-q1 |
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 |
$1$ |
\( 2 \) |
$1$ |
$10.55342183$ |
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-r1 |
1024.1-r |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
\( -2002968 a + 3470040 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 118 a - 203\) , \( 849 a - 1470\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(118a-203\right){x}+849a-1470$ |
| 4608.1-a1 |
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 |
$4$ |
\( 2 \) |
$1$ |
$4.308416424$ |
2.487465382 |
\( -2002968 a + 3470040 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 660 a - 1143\) , \( 12144 a - 21034\bigr] \) |
${y}^2={x}^{3}+\left(660a-1143\right){x}+12144a-21034$ |
| 4608.1-f1 |
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 |
$1$ |
\( 2^{2} \) |
$1.442267495$ |
$4.308416424$ |
3.587590466 |
\( -2002968 a + 3470040 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9192 a - 15921\) , \( 631254 a - 1093364\bigr] \) |
${y}^2={x}^{3}+\left(9192a-15921\right){x}+631254a-1093364$ |
| 4608.1-bb1 |
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 |
$1$ |
\( 2^{2} \) |
$1$ |
$8.616832848$ |
2.487465382 |
\( -2002968 a + 3470040 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9192 a - 15921\) , \( -631254 a + 1093364\bigr] \) |
${y}^2={x}^{3}+\left(9192a-15921\right){x}-631254a+1093364$ |
| 4608.1-be1 |
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 |
$1$ |
\( 2 \) |
$1.442267495$ |
$8.616832848$ |
3.587590466 |
\( -2002968 a + 3470040 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 660 a - 1143\) , \( -12144 a + 21034\bigr] \) |
${y}^2={x}^{3}+\left(660a-1143\right){x}-12144a+21034$ |
*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.
