| 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 |
| 1024.6-a1 |
1024.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.6 |
\( 2^{10} \) |
\( 2^{12} \) |
$1.33740$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.747220376$ |
$6.875185818$ |
1.941708926 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 1024.6-a2 |
1024.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.6 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.33740$ |
$(a), (-a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{4} \) |
$0.373610188$ |
$3.437592909$ |
1.941708926 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+4{x}$ |
| 1024.6-a3 |
1024.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.6 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.33740$ |
$(a), (-a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1.494440753$ |
$3.437592909$ |
1.941708926 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \) |
${y}^2={x}^{3}-11{x}-14$ |
| 1024.6-a4 |
1024.6-a |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.6 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.33740$ |
$(a), (-a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.494440753$ |
$3.437592909$ |
1.941708926 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \) |
${y}^2={x}^{3}-11{x}+14$ |
| 1024.6-b1 |
1024.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.6 |
\( 2^{10} \) |
\( 2^{12} \) |
$1.33740$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2^{2} \) |
$1$ |
$6.987926646$ |
1.320594006 |
\( -64 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+a{x}$ |
| 1024.6-b2 |
1024.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.6 |
\( 2^{10} \) |
\( 2^{21} \) |
$1.33740$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$3.493963323$ |
1.320594006 |
\( -17416 a + 20208 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 5\) , \( 3 a + 5\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-5\right){x}+3a+5$ |
| 1024.6-b3 |
1024.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.6 |
\( 2^{10} \) |
\( 2^{21} \) |
$1.33740$ |
$(a), (-a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{3} \) |
$1$ |
$3.493963323$ |
1.320594006 |
\( 17416 a + 2792 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -4 a\) , \( 8 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}-4a{x}+8a-8$ |
| 1024.6-b4 |
1024.6-b |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.6 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.33740$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$3.493963323$ |
1.320594006 |
\( 238328 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 10\) , \( 6 a - 8\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+10\right){x}+6a-8$ |
| 1024.6-c1 |
1024.6-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.6 |
\( 2^{10} \) |
\( 2^{12} \) |
$1.33740$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2Cs, 3Nn |
$1$ |
\( 2^{2} \) |
$1$ |
$6.987926646$ |
1.320594006 |
\( -64 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+a{x}$ |
| 1024.6-c2 |
1024.6-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.6 |
\( 2^{10} \) |
\( 2^{21} \) |
$1.33740$ |
$(a), (-a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2^{3} \) |
$1$ |
$3.493963323$ |
1.320594006 |
\( -17416 a + 20208 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 5\) , \( -3 a - 5\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-5\right){x}-3a-5$ |
| 1024.6-c3 |
1024.6-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.6 |
\( 2^{10} \) |
\( 2^{21} \) |
$1.33740$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$3.493963323$ |
1.320594006 |
\( 17416 a + 2792 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a\) , \( -8 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}-4a{x}-8a+8$ |
| 1024.6-c4 |
1024.6-c |
$4$ |
$4$ |
\(\Q(\sqrt{-7}) \) |
$2$ |
$[0, 1]$ |
1024.6 |
\( 2^{10} \) |
\( 2^{18} \) |
$1.33740$ |
$(a), (-a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2, 3$ |
2B, 3Nn |
$1$ |
\( 2 \) |
$1$ |
$3.493963323$ |
1.320594006 |
\( 238328 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 10\) , \( -6 a + 8\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+10\right){x}-6a+8$ |
*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.
