| 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 |
| 96.1-a1 |
96.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{8} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$3.261257214$ |
0.941443865 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 3 a - 9\) , \( -27\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(3a-9\right){x}-27$ |
| 96.1-c1 |
96.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( - 2^{9} \cdot 3^{8} \) |
$0.96894$ |
$(a+1), (a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$17.97674429$ |
1.297359770 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( a - 12\) , \( 2 a + 16\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(a-12\right){x}+2a+16$ |
| 288.1-b1 |
288.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{14} \) |
$1.27520$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$5.021722368$ |
1.449646380 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -79 a - 140\) , \( -1664 a - 2881\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-79a-140\right){x}-1664a-2881$ |
| 288.1-d1 |
288.1-d |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
288.1 |
\( 2^{5} \cdot 3^{2} \) |
\( - 2^{9} \cdot 3^{14} \) |
$1.27520$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.820391757$ |
$3.891545751$ |
1.843243885 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -79 a - 140\) , \( 1663 a + 2879\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-79a-140\right){x}+1663a+2879$ |
| 768.1-c1 |
768.1-c |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{21} \cdot 3^{8} \) |
$1.62956$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.211834002$ |
$8.988372149$ |
2.198599305 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a - 41\) , \( 11 a + 177\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-41\right){x}+11a+177$ |
| 768.1-n1 |
768.1-n |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
768.1 |
\( 2^{8} \cdot 3 \) |
\( - 2^{21} \cdot 3^{8} \) |
$1.62956$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.630628607$ |
1.882887730 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a - 41\) , \( -11 a - 177\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(10a-41\right){x}-11a-177$ |
| 2304.1-b1 |
2304.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{21} \cdot 3^{14} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.510861184$ |
1.449646380 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -312 a - 552\) , \( -13308 a - 23040\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-312a-552\right){x}-13308a-23040$ |
| 2304.1-e1 |
2304.1-e |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
2304.1 |
\( 2^{8} \cdot 3^{2} \) |
\( - 2^{21} \cdot 3^{14} \) |
$2.14462$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.945772875$ |
2.246784987 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( -312 a - 552\) , \( 13308 a + 23040\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(-312a-552\right){x}+13308a+23040$ |
| 3072.1-b1 |
3072.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{27} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.120342961$ |
$2.383075350$ |
2.917314563 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -48 a - 112\) , \( 1016 a + 1720\bigr] \) |
${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-48a-112\right){x}+1016a+1720$ |
| 3072.1-i1 |
3072.1-i |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{27} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$2.383075350$ |
2.751738390 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 122 a - 225\) , \( 1074 a - 1797\bigr] \) |
${y}^2={x}^{3}+{x}^{2}+\left(122a-225\right){x}+1074a-1797$ |
| 3072.1-br1 |
3072.1-br |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{27} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$1$ |
$3.075164358$ |
1.775446970 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -48 a - 112\) , \( -1016 a - 1720\bigr] \) |
${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-48a-112\right){x}-1016a-1720$ |
| 3072.1-cd1 |
3072.1-cd |
$6$ |
$8$ |
\(\Q(\sqrt{3}) \) |
$2$ |
$[2, 0]$ |
3072.1 |
\( 2^{10} \cdot 3 \) |
\( - 2^{27} \cdot 3^{8} \) |
$2.30454$ |
$(a+1), (a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.934993618$ |
$3.075164358$ |
3.320063175 |
\( -\frac{443186854}{81} a + \frac{767608522}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 122 a - 225\) , \( -1074 a + 1797\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+\left(122a-225\right){x}-1074a+1797$ |
*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.
