| 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 |
| 49.1-a1 |
49.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.49526$ |
$(7,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$4.796364224$ |
1.516743543 |
\( 8000 \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 2\) , \( -2 a - 24\bigr] \) |
${y}^2={x}^3+\left(-a+1\right){x}^2+\left(-4a+2\right){x}-2a-24$ |
| 49.1-a2 |
49.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
49.1 |
\( 7^{2} \) |
\( 7^{6} \) |
$1.49526$ |
$(7,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$4.796364224$ |
1.516743543 |
\( 8000 \) |
\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( a + 7\) , \( -a + 2\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(a+7\right){x}-a+2$ |
| 49.3-a1 |
49.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
49.3 |
\( 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$1.49526$ |
$(7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$4.796364224$ |
1.516743543 |
\( 8000 \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a + 2\) , \( 2 a - 24\bigr] \) |
${y}^2={x}^3+\left(a+1\right){x}^2+\left(4a+2\right){x}+2a-24$ |
| 49.3-a2 |
49.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
49.3 |
\( 7^{2} \) |
\( 7^{6} \) |
$1.49526$ |
$(7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$4.796364224$ |
1.516743543 |
\( 8000 \) |
\( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -2 a + 7\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a-1\right){x}^2+\left(-2a+7\right){x}+2$ |
| 529.1-a1 |
529.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
529.1 |
\( 23^{2} \) |
\( 2^{12} \cdot 23^{6} \) |
$2.71039$ |
$(23,a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.646045189$ |
0.836752959 |
\( 8000 \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -10 a - 25\) , \( -33 a + 24\bigr] \) |
${y}^2={x}^3+a{x}^2+\left(-10a-25\right){x}-33a+24$ |
| 529.1-a2 |
529.1-a |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
529.1 |
\( 23^{2} \) |
\( 23^{6} \) |
$2.71039$ |
$(23,a+6)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.646045189$ |
0.836752959 |
\( 8000 \) |
\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -4 a - 3\) , \( 2 a + 16\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}^2+\left(-4a-3\right){x}+2a+16$ |
| 529.3-a1 |
529.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
529.3 |
\( 23^{2} \) |
\( 23^{6} \) |
$2.71039$ |
$(23,a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.646045189$ |
0.836752959 |
\( 8000 \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 3 a - 3\) , \( -3 a + 16\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(3a-3\right){x}-3a+16$ |
| 529.3-a2 |
529.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
529.3 |
\( 23^{2} \) |
\( 2^{12} \cdot 23^{6} \) |
$2.71039$ |
$(23,a+17)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.646045189$ |
0.836752959 |
\( 8000 \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 25\) , \( 33 a + 24\bigr] \) |
${y}^2={x}^3-a{x}^2+\left(10a-25\right){x}+33a+24$ |
| 784.1-b1 |
784.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.99053$ |
$(2,a), (7,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.398182112$ |
0.758371771 |
\( 8000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a + 2\) , \( 2 a + 24\bigr] \) |
${y}^2={x}^3+\left(a-1\right){x}^2+\left(-4a+2\right){x}+2a+24$ |
| 784.1-b2 |
784.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{6} \) |
$2.99053$ |
$(2,a), (7,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.398182112$ |
0.758371771 |
\( 8000 \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -14 a + 17\) , \( 15 a - 69\bigr] \) |
${y}^2={x}^3+\left(a-1\right){x}^2+\left(-14a+17\right){x}+15a-69$ |
| 784.3-b1 |
784.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
784.3 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.99053$ |
$(2,a), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.398182112$ |
0.758371771 |
\( 8000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a + 2\) , \( -2 a + 24\bigr] \) |
${y}^2={x}^3+\left(-a-1\right){x}^2+\left(4a+2\right){x}-2a+24$ |
| 784.3-b2 |
784.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-10}) \) |
$2$ |
$[0, 1]$ |
784.3 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{6} \) |
$2.99053$ |
$(2,a), (7,a+5)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-8$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$5$ |
5Nn.1.1.1 |
$1$ |
\( 2^{2} \) |
$1$ |
$2.398182112$ |
0.758371771 |
\( 8000 \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 14 a + 17\) , \( -15 a - 69\bigr] \) |
${y}^2={x}^3+\left(-a-1\right){x}^2+\left(14a+17\right){x}-15a-69$ |
*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.
