| 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-a2 |
24.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3^{16} \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.325279868$ |
0.671250479 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -15 a + 29\) , \( 322 a - 557\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-15a+29\right){x}+322a-557$ |
| 24.1-b2 |
24.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3^{16} \) |
$0.68514$ |
$(a+1), (a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$5.683508517$ |
0.820343793 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -17 a + 26\) , \( -338 a + 584\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-17a+26\right){x}-338a+584$ |
| 144.1-a2 |
144.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{22} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a + 10\) , \( -68 a - 1\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a+10\right){x}-68a-1$ |
| 144.1-c2 |
144.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
144.1 |
\( 2^{4} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{22} \) |
$1.07231$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.098868579$ |
1.211782339 |
\( \frac{207646}{6561} \) |
\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -658 a + 1140\) , \( 88718 a - 153664\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(-658a+1140\right){x}+88718a-153664$ |
| 768.1-e2 |
768.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.841754258$ |
1.640687586 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 62 a + 111\) , \( 2637 a + 4569\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(62a+111\right){x}+2637a+4569$ |
| 768.1-l2 |
768.1-l |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$1.079273864$ |
$1.162639934$ |
2.897852395 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 62 a + 111\) , \( -2637 a - 4569\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(62a+111\right){x}-2637a-4569$ |
| 2304.1-q2 |
2304.1-q |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{22} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.786181258$ |
$1.049434289$ |
3.376245242 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( 48\) , \( -540 a\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+48{x}-540a$ |
| 2304.1-bb2 |
2304.1-bb |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{22} \) |
$2.14462$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$2.786181258$ |
$1.049434289$ |
3.376245242 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 48\) , \( 540 a\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+48{x}+540a$ |
| 3072.1-e2 |
3072.1-e |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{28} \cdot 3^{16} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.285289264$ |
2.968248410 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -32 a + 64\) , \( -1080 a + 1800\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-32a+64\right){x}-1080a+1800$ |
| 3072.1-f2 |
3072.1-f |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{28} \cdot 3^{16} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.719487697$ |
$1.285289264$ |
2.760090861 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 32 a + 64\) , \( -1080 a - 1800\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(32a+64\right){x}-1080a-1800$ |
| 3072.1-bt2 |
3072.1-bt |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{28} \cdot 3^{16} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$1.285289264$ |
2.968248410 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 32 a + 64\) , \( 1080 a + 1800\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(32a+64\right){x}+1080a+1800$ |
| 3072.1-cc2 |
3072.1-cc |
$8$ |
$16$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( 2^{28} \cdot 3^{16} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$3.719487697$ |
$1.285289264$ |
2.760090861 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -32 a + 64\) , \( 1080 a - 1800\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-32a+64\right){x}+1080a-1800$ |
*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.
