| 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 |
| 64.1-a3 |
64.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$0.87554$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$13.75037163$ |
0.992347595 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 11 a - 17\) , \( 17 a - 29\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(11a-17\right){x}+17a-29$ |
| 64.1-a4 |
64.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
64.1 |
\( 2^{6} \) |
\( 2^{6} \) |
$0.87554$ |
$(a+1)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$55.00148654$ |
0.992347595 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 10 a - 19\) , \( -36 a + 61\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(10a-19\right){x}-36a+61$ |
| 256.1-f3 |
256.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{18} \) |
$1.23820$ |
$(a+1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.444312937$ |
$6.875185818$ |
1.763651500 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 44 a - 77\) , \( 210 a - 364\bigr] \) |
${y}^2={x}^{3}+\left(44a-77\right){x}+210a-364$ |
| 256.1-f4 |
256.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
256.1 |
\( 2^{8} \) |
\( 2^{18} \) |
$1.23820$ |
$(a+1)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.444312937$ |
$27.50074327$ |
1.763651500 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 44 a - 77\) , \( -210 a + 364\bigr] \) |
${y}^2={x}^{3}+\left(44a-77\right){x}-210a+364$ |
| 576.1-c3 |
576.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{6} \) |
$1.51647$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.501182392$ |
$15.87756153$ |
2.297148049 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 462 a - 798\) , \( 6693 a - 11592\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(462a-798\right){x}+6693a-11592$ |
| 576.1-c4 |
576.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{6} \) |
$1.51647$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$0.501182392$ |
$15.87756153$ |
2.297148049 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 461 a - 800\) , \( -7493 a + 12977\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(461a-800\right){x}-7493a+12977$ |
| 1024.1-h3 |
1024.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.403391428 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 330 a - 572\) , \( 4284 a - 7420\bigr] \) |
${y}^2={x}^{3}+\left(330a-572\right){x}+4284a-7420$ |
| 1024.1-h4 |
1024.1-h |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.403391428 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 330 a - 572\) , \( -4284 a + 7420\bigr] \) |
${y}^2={x}^{3}+\left(330a-572\right){x}-4284a+7420$ |
| 1024.1-m3 |
1024.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.403391428 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 22 a - 44\) , \( 84 a - 140\bigr] \) |
${y}^2={x}^{3}+\left(22a-44\right){x}+84a-140$ |
| 1024.1-m4 |
1024.1-m |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
1024.1 |
\( 2^{10} \) |
\( 2^{24} \) |
$1.75107$ |
$(a+1)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$9.722981027$ |
1.403391428 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 22 a - 44\) , \( -84 a + 140\bigr] \) |
${y}^2={x}^{3}+\left(22a-44\right){x}-84a+140$ |
| 2304.1-c3 |
2304.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$7.938780765$ |
2.291728606 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -33\) , \( -42 a\bigr] \) |
${y}^2={x}^{3}-33{x}-42a$ |
| 2304.1-c4 |
2304.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{18} \cdot 3^{6} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1$ |
$7.938780765$ |
2.291728606 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -33\) , \( 42 a\bigr] \) |
${y}^2={x}^{3}-33{x}+42a$ |
*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.
