| 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-a7 |
24.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.325279868$ |
0.671250479 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 385 a - 671\) , \( 5582 a - 9681\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(385a-671\right){x}+5582a-9681$ |
| 24.1-b7 |
24.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$22.73403407$ |
0.820343793 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 383 a - 674\) , \( -5198 a + 9008\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(383a-674\right){x}-5198a+9008$ |
| 144.1-a7 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{10} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.197737158$ |
1.211782339 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 290\) , \( -1040 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-290\right){x}-1040a-1$ |
| 144.1-c7 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{10} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$4.197737158$ |
1.211782339 |
\( \frac{3065617154}{9} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 16142 a - 27960\) , \( 1464590 a - 2536744\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(16142a-27960\right){x}+1464590a-2536744$ |
| 768.1-e7 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$11.36701703$ |
1.640687586 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -1538 a - 2689\) , \( 43117 a + 74761\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-1538a-2689\right){x}+43117a+74761$ |
| 768.1-l7 |
768.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.079273864$ |
$1.162639934$ |
2.897852395 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1538 a - 2689\) , \( -43117 a - 74761\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1538a-2689\right){x}-43117a-74761$ |
| 2304.1-q7 |
2304.1-q |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{10} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.786181258$ |
$2.098868579$ |
3.376245242 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -1152\) , \( -8316 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}-1152{x}-8316a$ |
| 2304.1-bb7 |
2304.1-bb |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{10} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.786181258$ |
$2.098868579$ |
3.376245242 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -1152\) , \( 8316 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}-1152{x}+8316a$ |
| 3072.1-e7 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{28} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.570578528$ |
2.968248410 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 768 a - 1536\) , \( -16632 a + 27720\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(768a-1536\right){x}-16632a+27720$ |
| 3072.1-f7 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{28} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.929871924$ |
$2.570578528$ |
2.760090861 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -768 a - 1536\) , \( -16632 a - 27720\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-768a-1536\right){x}-16632a-27720$ |
| 3072.1-bt7 |
3072.1-bt |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{28} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.570578528$ |
2.968248410 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -768 a - 1536\) , \( 16632 a + 27720\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-768a-1536\right){x}+16632a+27720$ |
| 3072.1-cc7 |
3072.1-cc |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{28} \cdot 3^{4} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.929871924$ |
$2.570578528$ |
2.760090861 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 768 a - 1536\) , \( 16632 a - 27720\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(768a-1536\right){x}+16632a-27720$ |
*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.
