| 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 |
| 24.1-a6 |
24.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$37.20447790$ |
0.671250479 |
\( \frac{28756228}{3} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 65 a - 111\) , \( -348 a + 603\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(65a-111\right){x}-348a+603$ |
| 24.1-b6 |
24.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$5.683508517$ |
0.820343793 |
\( \frac{28756228}{3} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 63 a - 114\) , \( 412 a - 716\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(63a-114\right){x}+412a-716$ |
| 144.1-a6 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.395474317$ |
1.211782339 |
\( \frac{28756228}{3} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 50\) , \( 82 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-50\right){x}+82a-1$ |
| 144.1-c6 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$8.395474317$ |
1.211782339 |
\( \frac{28756228}{3} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 2702 a - 4680\) , \( -101392 a + 175616\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(2702a-4680\right){x}-101392a+175616$ |
| 768.1-e6 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$2.841754258$ |
1.640687586 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 258 a - 449\) , \( 3043 a - 5271\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(258a-449\right){x}+3043a-5271$ |
| 768.1-l6 |
768.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$0.539636932$ |
$18.60223895$ |
2.897852395 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 258 a - 449\) , \( -3043 a + 5271\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(258a-449\right){x}-3043a+5271$ |
| 2304.1-q6 |
2304.1-q |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.393090629$ |
$4.197737158$ |
3.376245242 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 10808 a - 18720\) , \( 811136 a - 1404928\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(10808a-18720\right){x}+811136a-1404928$ |
| 2304.1-bb6 |
2304.1-bb |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.393090629$ |
$4.197737158$ |
3.376245242 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 10808 a - 18720\) , \( -811136 a + 1404928\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(10808a-18720\right){x}-811136a+1404928$ |
| 3072.1-e6 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{26} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$5.141157056$ |
2.968248410 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 26892 a - 46576\) , \( 3152252 a - 5459860\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(26892a-46576\right){x}+3152252a-5459860$ |
| 3072.1-f6 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{26} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.859743848$ |
$5.141157056$ |
2.760090861 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1930 a - 3345\) , \( 60126 a - 104139\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(1930a-3345\right){x}+60126a-104139$ |
| 3072.1-bt6 |
3072.1-bt |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{26} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$5.141157056$ |
2.968248410 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1930 a - 3345\) , \( -60126 a + 104139\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(1930a-3345\right){x}-60126a+104139$ |
| 3072.1-cc6 |
3072.1-cc |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{26} \cdot 3^{2} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1.859743848$ |
$5.141157056$ |
2.760090861 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 26892 a - 46576\) , \( -3152252 a + 5459860\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(26892a-46576\right){x}-3152252a+5459860$ |
*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.
