| 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 |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{8} \) |
$1.37029$ |
$(2,a), (3,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.209555911$ |
$4.690728597$ |
1.605183135 |
\( \frac{97336}{81} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 7\) , \( 0\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+7{x}$ |
| 96.1-a2 |
96.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{16} \) |
$1.37029$ |
$(2,a), (3,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.838223645$ |
$4.690728597$ |
1.605183135 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -21\) , \( -20\bigr] \) |
${y}^2={x}^3-21{x}-20$ |
| 96.1-a3 |
96.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.37029$ |
$(2,a), (3,a)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.838223645$ |
$4.690728597$ |
1.605183135 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( -2\bigr] \) |
${y}^2={x}^3-{x}^2-4{x}-2$ |
| 96.1-a4 |
96.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{2} \) |
$1.37029$ |
$(2,a), (3,a)$ |
$2$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.838223645$ |
$4.690728597$ |
1.605183135 |
\( \frac{7301384}{3} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -6\) , \( 15\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-6{x}+15$ |
| 96.1-b1 |
96.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{18} \cdot 3^{8} \) |
$1.37029$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.690728597$ |
1.914981930 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 8\) , \( -8\bigr] \) |
${y}^2={x}^3-{x}^2+8{x}-8$ |
| 96.1-b2 |
96.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$1.37029$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$4.690728597$ |
1.914981930 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}^2-2{x}$ |
| 96.1-b3 |
96.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{24} \cdot 3^{2} \) |
$1.37029$ |
$(2,a), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$4.690728597$ |
1.914981930 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -17\) , \( 33\bigr] \) |
${y}^2={x}^3-{x}^2-17{x}+33$ |
| 96.1-b4 |
96.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$1.37029$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.690728597$ |
1.914981930 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -32\) , \( -60\bigr] \) |
${y}^2={x}^3-{x}^2-32{x}-60$ |
| 96.1-c1 |
96.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{8} \) |
$1.37029$ |
$(2,a), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.690728597$ |
1.914981930 |
\( \frac{97336}{81} \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 2\) , \( -1\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2+2{x}-1$ |
| 96.1-c2 |
96.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{16} \) |
$1.37029$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.690728597$ |
1.914981930 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -21\) , \( 20\bigr] \) |
${y}^2={x}^3-21{x}+20$ |
| 96.1-c3 |
96.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{2} \) |
$1.37029$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.690728597$ |
1.914981930 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4\) , \( 2\bigr] \) |
${y}^2={x}^3+{x}^2-4{x}+2$ |
| 96.1-c4 |
96.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{6} \cdot 3^{2} \) |
$1.37029$ |
$(2,a), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$4.690728597$ |
1.914981930 |
\( \frac{7301384}{3} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( -6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-5{x}-6$ |
| 96.1-d1 |
96.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{18} \cdot 3^{8} \) |
$1.37029$ |
$(2,a), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.690728597$ |
1.914981930 |
\( \frac{97336}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 8\) , \( 8\bigr] \) |
${y}^2={x}^3+{x}^2+8{x}+8$ |
| 96.1-d2 |
96.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{12} \cdot 3^{4} \) |
$1.37029$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.690728597$ |
1.914981930 |
\( \frac{21952}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}^2-2{x}$ |
| 96.1-d3 |
96.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{24} \cdot 3^{2} \) |
$1.37029$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.690728597$ |
1.914981930 |
\( \frac{140608}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -17\) , \( -33\bigr] \) |
${y}^2={x}^3+{x}^2-17{x}-33$ |
| 96.1-d4 |
96.1-d |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
96.1 |
\( 2^{5} \cdot 3 \) |
\( 2^{18} \cdot 3^{2} \) |
$1.37029$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$4.690728597$ |
1.914981930 |
\( \frac{7301384}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -32\) , \( 60\bigr] \) |
${y}^2={x}^3+{x}^2-32{x}+60$ |
*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.
