| 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 |
| 576.1-a1 |
576.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{7} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.83277367$ |
1.563576199 |
\( -\frac{1842168016}{3} a + 1063576200 \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 208 a - 360\) , \( -2209 a + 3826\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(208a-360\right){x}-2209a+3826$ |
| 576.1-a2 |
576.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{14} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.416386836$ |
1.563576199 |
\( \frac{97336}{81} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -323 a + 556\) , \( 2832 a - 4907\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-323a+556\right){x}+2832a-4907$ |
| 576.1-a3 |
576.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.83277367$ |
1.563576199 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 28 a - 48\) , \( 74 a - 128\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(28a-48\right){x}+74a-128$ |
| 576.1-a4 |
576.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.83277367$ |
1.563576199 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -12\) , \( -6 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-12{x}-6a$ |
| 576.1-a5 |
576.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{8} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.83277367$ |
1.563576199 |
\( \frac{7301384}{3} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 1358 a - 2352\) , \( 35447 a - 61396\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(1358a-2352\right){x}+35447a-61396$ |
| 576.1-a6 |
576.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{7} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.416386836$ |
1.563576199 |
\( \frac{1842168016}{3} a + 1063576200 \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -3 a - 2\) , \( -102 a + 171\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-3a-2\right){x}-102a+171$ |
| 576.1-b1 |
576.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{7} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.416386836$ |
1.563576199 |
\( -\frac{1842168016}{3} a + 1063576200 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 208 a - 360\) , \( 2209 a - 3826\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(208a-360\right){x}+2209a-3826$ |
| 576.1-b2 |
576.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{14} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.416386836$ |
1.563576199 |
\( \frac{97336}{81} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -323 a + 556\) , \( -2833 a + 4905\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-323a+556\right){x}-2833a+4905$ |
| 576.1-b3 |
576.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{10} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.83277367$ |
1.563576199 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 28 a - 48\) , \( -74 a + 128\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(28a-48\right){x}-74a+128$ |
| 576.1-b4 |
576.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{8} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$10.83277367$ |
1.563576199 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -12\) , \( 6 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-12{x}+6a$ |
| 576.1-b5 |
576.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{6} \cdot 3^{8} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.83277367$ |
1.563576199 |
\( \frac{7301384}{3} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 1358 a - 2352\) , \( -35447 a + 61396\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1358a-2352\right){x}-35447a+61396$ |
| 576.1-b6 |
576.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( - 2^{6} \cdot 3^{7} \) |
$1.51647$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$10.83277367$ |
1.563576199 |
\( \frac{1842168016}{3} a + 1063576200 \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -3 a - 2\) , \( 101 a - 173\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-2\right){x}+101a-173$ |
| 576.1-c1 |
576.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.51647$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$0.501182392$ |
$7.938780765$ |
2.297148049 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 3\) , \( 0\bigr] \) |
${y}^2={x}^{3}+3{x}$ |
| 576.1-c2 |
576.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
576.1 |
\( 2^{6} \cdot 3^{2} \) |
\( 2^{12} \cdot 3^{6} \) |
$1.51647$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.250591196$ |
$15.87756153$ |
2.297148049 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a - 21\) , \( 0\bigr] \) |
${y}^2={x}^{3}+\left(12a-21\right){x}$ |
| 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 |
\( 287496 \) |
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 461 a - 800\) , \( -7493 a + 12977\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(461a-800\right){x}-7493a+12977$ |
*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.
