| 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 |
| 1024.1-c1 |
1024.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{12} \) |
$1.67652$ |
$(2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.518236630 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}-{x}$ |
| 1024.1-c2 |
1024.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.67652$ |
$(2)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$3.437592909$ |
0.518236630 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+4{x}$ |
| 4096.1-d1 |
4096.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{12} \) |
$2.37096$ |
$(2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$2.126572485$ |
$6.875185818$ |
4.408271033 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}$ |
| 4096.1-d2 |
4096.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
4096.1 |
\( 2^{12} \) |
\( 2^{24} \) |
$2.37096$ |
$(2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$4.253144970$ |
$3.437592909$ |
4.408271033 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \) |
${y}^2={x}^{3}-4{x}$ |
| 9216.1-c1 |
9216.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.90383$ |
$(-a), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.706570460$ |
$3.969390382$ |
4.084902455 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+3\right){x}$ |
| 9216.1-c2 |
9216.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.1 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.90383$ |
$(-a), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.853285230$ |
$1.984695191$ |
4.084902455 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 12\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a-12\right){x}$ |
| 9216.3-c1 |
9216.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.3 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$2.90383$ |
$(a-1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.706570460$ |
$3.969390382$ |
4.084902455 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a+2\right){x}$ |
| 9216.3-c2 |
9216.3-c |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
9216.3 |
\( 2^{10} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$2.90383$ |
$(a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.853285230$ |
$1.984695191$ |
4.084902455 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 8\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a-8\right){x}$ |
| 25600.1-d1 |
25600.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{9} \) |
$3.74882$ |
$(-a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.007086908$ |
$2.056160146$ |
2.497396716 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 11\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a+11\right){x}$ |
| 25600.1-d2 |
25600.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{9} \) |
$3.74882$ |
$(-a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$2.014173817$ |
$1.028080073$ |
2.497396716 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a - 44\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(16a-44\right){x}$ |
| 25600.1-e1 |
25600.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{6} \) |
$3.74882$ |
$(-a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1.425374527$ |
$1.537338284$ |
5.285573062 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a - 8\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(12a-8\right){x}$ |
| 25600.1-e2 |
25600.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$3.74882$ |
$(-a-1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.850749055$ |
$3.074676569$ |
5.285573062 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a + 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-3a+2\right){x}$ |
| 25600.1-f1 |
25600.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{3} \) |
$3.74882$ |
$(-a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$4.597713860$ |
2.772525776 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}$ |
| 25600.1-f2 |
25600.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.1 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{3} \) |
$3.74882$ |
$(-a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$2.298856930$ |
2.772525776 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a + 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a+4\right){x}$ |
| 25600.3-d1 |
25600.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.3 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{9} \) |
$3.74882$ |
$(a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$2.014173817$ |
$1.028080073$ |
2.497396716 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a - 28\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-16a-28\right){x}$ |
| 25600.3-d2 |
25600.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.3 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{9} \) |
$3.74882$ |
$(a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.007086908$ |
$2.056160146$ |
2.497396716 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a + 7\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a+7\right){x}$ |
| 25600.3-e1 |
25600.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.3 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{6} \) |
$3.74882$ |
$(a-2), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1.425374527$ |
$1.537338284$ |
5.285573062 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a + 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-12a+4\right){x}$ |
| 25600.3-e2 |
25600.3-e |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.3 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{6} \) |
$3.74882$ |
$(a-2), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.850749055$ |
$3.074676569$ |
5.285573062 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(3a-1\right){x}$ |
| 25600.3-f1 |
25600.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.3 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{24} \cdot 5^{3} \) |
$3.74882$ |
$(a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$2.298856930$ |
2.772525776 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 8\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a+8\right){x}$ |
| 25600.3-f2 |
25600.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
25600.3 |
\( 2^{10} \cdot 5^{2} \) |
\( 2^{12} \cdot 5^{3} \) |
$3.74882$ |
$(a-2), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$4.597713860$ |
2.772525776 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-2\right){x}$ |
| 36864.1-d1 |
36864.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$4.10663$ |
$(-a), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.696305545$ |
$1.508042231$ |
2.532835602 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 a + 12\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(8a+12\right){x}$ |
| 36864.1-d2 |
36864.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{9} \) |
$4.10663$ |
$(-a), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.392611090$ |
$3.016084463$ |
2.532835602 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a-3\right){x}$ |
| 36864.1-e1 |
36864.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$4.10663$ |
$(-a), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.612005765$ |
1.575098740 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a\) , \( 0\bigr] \) |
${y}^2={x}^{3}-4a{x}$ |
| 36864.1-e2 |
36864.1-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$4.10663$ |
$(-a), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$5.224011530$ |
1.575098740 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+a{x}$ |
| 36864.1-f1 |
36864.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$4.10663$ |
$(-a), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$5.224011530$ |
1.575098740 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a\) , \( 0\bigr] \) |
${y}^2={x}^{3}-a{x}$ |
| 36864.1-f2 |
36864.1-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$4.10663$ |
$(-a), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.612005765$ |
1.575098740 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a\) , \( 0\bigr] \) |
${y}^2={x}^{3}+4a{x}$ |
| 36864.1-g1 |
36864.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$4.10663$ |
$(-a), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$3.969390382$ |
1.196816231 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-3\right){x}$ |
| 36864.1-g2 |
36864.1-g |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$4.10663$ |
$(-a), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.984695191$ |
1.196816231 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 12\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a+12\right){x}$ |
| 36864.1-h1 |
36864.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{9} \) |
$4.10663$ |
$(-a), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$4.868571633$ |
$3.016084463$ |
8.854799193 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a+3\right){x}$ |
| 36864.1-h2 |
36864.1-h |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.1 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$4.10663$ |
$(-a), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$2.434285816$ |
$1.508042231$ |
8.854799193 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a - 12\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-8a-12\right){x}$ |
| 36864.3-d1 |
36864.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.3 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$4.10663$ |
$(a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$0.696305545$ |
$1.508042231$ |
2.532835602 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a + 20\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-8a+20\right){x}$ |
| 36864.3-d2 |
36864.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.3 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{9} \) |
$4.10663$ |
$(a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1.392611090$ |
$3.016084463$ |
2.532835602 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(2a-5\right){x}$ |
| 36864.3-e1 |
36864.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.3 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$4.10663$ |
$(a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$5.224011530$ |
1.575098740 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( a - 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}$ |
| 36864.3-e2 |
36864.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.3 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$4.10663$ |
$(a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.612005765$ |
1.575098740 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-4a+4\right){x}$ |
| 36864.3-f1 |
36864.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.3 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$4.10663$ |
$(a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$3.969390382$ |
1.196816231 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 2\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a-2\right){x}$ |
| 36864.3-f2 |
36864.3-f |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.3 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{6} \) |
$4.10663$ |
$(a-1), (2)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$1.984695191$ |
1.196816231 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a + 8\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a+8\right){x}$ |
| 36864.3-g1 |
36864.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.3 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{3} \) |
$4.10663$ |
$(a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$2.612005765$ |
1.575098740 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 4\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(4a-4\right){x}$ |
| 36864.3-g2 |
36864.3-g |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.3 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{3} \) |
$4.10663$ |
$(a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$5.224011530$ |
1.575098740 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a + 1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}$ |
| 36864.3-h1 |
36864.3-h |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.3 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{9} \) |
$4.10663$ |
$(a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$4.868571633$ |
$3.016084463$ |
8.854799193 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 5\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(-2a+5\right){x}$ |
| 36864.3-h2 |
36864.3-h |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
36864.3 |
\( 2^{12} \cdot 3^{2} \) |
\( 2^{24} \cdot 3^{9} \) |
$4.10663$ |
$(a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$2.434285816$ |
$1.508042231$ |
8.854799193 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 8 a - 20\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(8a-20\right){x}$ |
*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.
