| 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-c2 |
512.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.47247$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.68304578$ |
2.263652675 |
\( 10976 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a - 8\) , \( 12 a + 20\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-8\right){x}+12a+20$ |
| 512.1-d2 |
512.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.47247$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$15.68304578$ |
2.263652675 |
\( 10976 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a - 8\) , \( -12 a + 20\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(4a-8\right){x}-12a+20$ |
| 512.1-e2 |
512.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.47247$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.181508768$ |
$15.68304578$ |
1.643491233 |
\( 10976 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 8\) , \( -12 a - 20\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-8\right){x}-12a-20$ |
| 512.1-f2 |
512.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
512.1 |
\( 2^{9} \) |
\( 2^{20} \) |
$1.47247$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.181508768$ |
$15.68304578$ |
1.643491233 |
\( 10976 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a - 8\) , \( 12 a - 20\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a-8\right){x}+12a-20$ |
| 1024.1-e2 |
1024.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$32.58604536$ |
2.351695258 |
\( 10976 \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 2\bigr] \) |
${y}^2={x}^{3}-{x}^{2}-2{x}+2$ |
| 1024.1-f2 |
1024.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.816471691$ |
$15.09590514$ |
3.558030500 |
\( 10976 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a - 15\) , \( 21 a - 37\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-15\right){x}+21a-37$ |
| 1024.1-o2 |
1024.1-o |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$15.09590514$ |
1.089453112 |
\( 10976 \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( -2\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-2{x}-2$ |
| 1024.1-p2 |
1024.1-p |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{14} \) |
$1.75107$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2 \) |
$0.216165582$ |
$32.58604536$ |
2.033422299 |
\( 10976 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a - 15\) , \( -21 a + 37\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-15\right){x}-21a+37$ |
| 4608.1-h2 |
4608.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
$1$ |
\( 2^{2} \) |
$1$ |
$6.162877468$ |
1.779069482 |
\( 10976 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -14 a - 27\) , \( -47 a - 82\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-14a-27\right){x}-47a-82$ |
| 4608.1-i2 |
4608.1-i |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
$1$ |
\( 2^{2} \) |
$1$ |
$6.162877468$ |
1.779069482 |
\( 10976 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 14 a - 27\) , \( 47 a - 82\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(14a-27\right){x}+47a-82$ |
| 4608.1-v2 |
4608.1-v |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
$1$ |
\( 2^{3} \) |
$0.256481616$ |
$13.30319731$ |
3.939867736 |
\( 10976 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 14 a - 27\) , \( -47 a + 82\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(14a-27\right){x}-47a+82$ |
| 4608.1-ba2 |
4608.1-ba |
$2$ |
$2$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
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 |
$1$ |
\( 2^{3} \) |
$0.256481616$ |
$13.30319731$ |
3.939867736 |
\( 10976 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -14 a - 27\) , \( 47 a + 82\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-14a-27\right){x}+47a+82$ |
*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.
