| 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-a1 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$0.96894$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
0.742062102 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \) |
${y}^2={x}^3-{x}^2+16{x}-180$ |
| 24.1-a2 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$0.96894$ |
$(2,a), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
0.742062102 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}^2+{x}$ |
| 24.1-a3 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$0.96894$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
0.742062102 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \) |
${y}^2={x}^3-{x}^2-4{x}+4$ |
| 24.1-a4 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{20} \cdot 3^{8} \) |
$0.96894$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.635347017$ |
0.742062102 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \) |
${y}^2={x}^3-{x}^2-24{x}-36$ |
| 24.1-a5 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$0.96894$ |
$(2,a), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$3.635347017$ |
0.742062102 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \) |
${y}^2={x}^3-{x}^2-64{x}+220$ |
| 24.1-a6 |
24.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$0.96894$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
0.742062102 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \) |
${y}^2={x}^3-{x}^2-384{x}-2772$ |
| 24.1-b1 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3^{16} \) |
$0.96894$ |
$(2,a), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$1.817673508$ |
1.484124205 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 7\) , \( -21\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+7{x}-21$ |
| 24.1-b2 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$0.96894$ |
$(2,a), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$7.270694035$ |
1.484124205 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 3\bigr] \) |
${y}^2={x}^3+{x}^2+3{x}+3$ |
| 24.1-b3 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$0.96894$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$7.270694035$ |
1.484124205 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 2\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+2{x}+2$ |
| 24.1-b4 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$0.96894$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$3.635347017$ |
1.484124205 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -3\) , \( -3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-3{x}-3$ |
| 24.1-b5 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$0.96894$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$3.635347017$ |
1.484124205 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -13\) , \( 29\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-13{x}+29$ |
| 24.1-b6 |
24.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
24.1 |
\( 2^{3} \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$0.96894$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.817673508$ |
1.484124205 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -93\) , \( -345\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-93{x}-345$ |
| 32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$1.04119$ |
$(2,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.888625874$ |
$6.875185818$ |
1.247089935 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}$ |
| 32.1-a2 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$1.04119$ |
$(2,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.777251749$ |
$6.875185818$ |
1.247089935 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^3+4{x}$ |
| 32.1-a3 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$1.04119$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.444312937$ |
$6.875185818$ |
1.247089935 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \) |
${y}^2={x}^3-11{x}-14$ |
| 32.1-a4 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$1.04119$ |
$(2,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.777251749$ |
$6.875185818$ |
1.247089935 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \) |
${y}^2={x}^3-11{x}+14$ |
| 32.1-b1 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$1.04119$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 2 \) |
$1$ |
$6.875185818$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \) |
${y}^2={x}^3-4{x}$ |
| 32.1-b2 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$1.04119$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
1.403391428 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}$ |
| 32.1-b3 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$1.04119$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 2 \) |
$1$ |
$6.875185818$ |
1.403391428 |
\( 287496 \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -2\) , \( 3\bigr] \) |
${y}^2+a{x}{y}={x}^3-2{x}+3$ |
| 32.1-b4 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$1.04119$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
1.403391428 |
\( 287496 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 1\) , \( 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}+1$ |
| 36.1-a1 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{18} \) |
$1.07231$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \) |
$0.653234677$ |
$5.108115717$ |
1.362242211 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -27\bigr] \) |
${y}^2={x}^3-27$ |
| 36.1-a2 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{6} \) |
$1.07231$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1.959704032$ |
$5.108115717$ |
1.362242211 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 1\bigr] \) |
${y}^2={x}^3+1$ |
| 36.1-a3 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{6} \) |
$1.07231$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.979852016$ |
$5.108115717$ |
1.362242211 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15\) , \( 22\bigr] \) |
${y}^2={x}^3-15{x}+22$ |
| 36.1-a4 |
36.1-a |
$4$ |
$6$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
36.1 |
\( 2^{2} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{6} \) |
$1.07231$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \) |
$0.326617338$ |
$5.108115717$ |
1.362242211 |
\( 54000 \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( 0\) , \( 6\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+6$ |
| 48.1-a1 |
48.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{10} \cdot 3^{16} \) |
$1.15227$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$1.817673508$ |
1.484124205 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 6\) , \( 18\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+6{x}+18$ |
| 48.1-a2 |
48.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.15227$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$7.270694035$ |
1.484124205 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 3\) , \( -3\bigr] \) |
${y}^2={x}^3-{x}^2+3{x}-3$ |
| 48.1-a3 |
48.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{4} \cdot 3^{4} \) |
$1.15227$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$7.270694035$ |
1.484124205 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2+{x}$ |
| 48.1-a4 |
48.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{8} \cdot 3^{8} \) |
$1.15227$ |
$(2,a), (3,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$3.635347017$ |
1.484124205 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -4\) , \( 10\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-4{x}+10$ |
| 48.1-a5 |
48.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$1.15227$ |
$(2,a), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$3.635347017$ |
1.484124205 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -14\) , \( -12\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-14{x}-12$ |
| 48.1-a6 |
48.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{10} \cdot 3^{4} \) |
$1.15227$ |
$(2,a), (3,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$1.817673508$ |
1.484124205 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -94\) , \( 442\bigr] \) |
${y}^2+a{x}{y}={x}^3-{x}^2-94{x}+442$ |
| 48.1-b1 |
48.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{22} \cdot 3^{16} \) |
$1.15227$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.079273864$ |
$1.817673508$ |
1.601776466 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 16\) , \( 180\bigr] \) |
${y}^2={x}^3+{x}^2+16{x}+180$ |
| 48.1-b2 |
48.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{8} \cdot 3^{2} \) |
$1.15227$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$0.539636932$ |
$7.270694035$ |
1.601776466 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}^2+{x}$ |
| 48.1-b3 |
48.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{16} \cdot 3^{4} \) |
$1.15227$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1.079273864$ |
$7.270694035$ |
1.601776466 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -4\) , \( -4\bigr] \) |
${y}^2={x}^3+{x}^2-4{x}-4$ |
| 48.1-b4 |
48.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{20} \cdot 3^{8} \) |
$1.15227$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.158547729$ |
$3.635347017$ |
1.601776466 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -24\) , \( 36\bigr] \) |
${y}^2={x}^3+{x}^2-24{x}+36$ |
| 48.1-b5 |
48.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{20} \cdot 3^{2} \) |
$1.15227$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$0.539636932$ |
$3.635347017$ |
1.601776466 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -64\) , \( -220\bigr] \) |
${y}^2={x}^3+{x}^2-64{x}-220$ |
| 48.1-b6 |
48.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
48.1 |
\( 2^{4} \cdot 3 \) |
\( 2^{22} \cdot 3^{4} \) |
$1.15227$ |
$(2,a), (3,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.079273864$ |
$1.817673508$ |
1.601776466 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -384\) , \( 2772\bigr] \) |
${y}^2={x}^3+{x}^2-384{x}+2772$ |
| 75.1-a1 |
75.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{20} \cdot 5^{6} \) |
$1.28828$ |
$(3,a), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$1.163923753$ |
$0.870223358$ |
0.827007861 |
\( -\frac{873722816}{59049} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -42 a + 20\) , \( 117 a - 294\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+\left(a-1\right){x}^2+\left(-42a+20\right){x}+117a-294$ |
| 75.1-a2 |
75.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{6} \) |
$1.28828$ |
$(3,a), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{2} \) |
$0.232784750$ |
$4.351116790$ |
0.827007861 |
\( \frac{64}{9} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -2 a\) , \( 2\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^3+\left(a-1\right){x}^2-2a{x}+2$ |
| 75.1-a3 |
75.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{2} \cdot 5^{6} \) |
$1.28828$ |
$(3,a), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$0.116392375$ |
$4.351116790$ |
0.827007861 |
\( \frac{85184}{3} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8 a + 2\) , \( -2 a + 40\bigr] \) |
${y}^2={x}^3+\left(a-1\right){x}^2+\left(-8a+2\right){x}-2a+40$ |
| 75.1-a4 |
75.1-a |
$4$ |
$10$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{10} \cdot 5^{6} \) |
$1.28828$ |
$(3,a), (5,a+2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$0.581961876$ |
$0.870223358$ |
0.827007861 |
\( \frac{58591911104}{243} \) |
\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -648 a + 322\) , \( 5078 a - 21000\bigr] \) |
${y}^2={x}^3+\left(a-1\right){x}^2+\left(-648a+322\right){x}+5078a-21000$ |
| 75.1-b1 |
75.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{20} \cdot 5^{6} \) |
$1.28828$ |
$(3,a), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.870223358$ |
3.552671983 |
\( -\frac{873722816}{59049} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -160 a + 78\) , \( 534 a - 3156\bigr] \) |
${y}^2={x}^3+\left(-a+1\right){x}^2+\left(-160a+78\right){x}+534a-3156$ |
| 75.1-b2 |
75.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 2^{12} \cdot 3^{4} \cdot 5^{6} \) |
$1.28828$ |
$(3,a), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.351116790$ |
3.552671983 |
\( \frac{64}{9} \) |
\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2\) , \( -2 a + 12\bigr] \) |
${y}^2={x}^3+\left(-a+1\right){x}^2-2{x}-2a+12$ |
| 75.1-b3 |
75.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{6} \) |
$1.28828$ |
$(3,a), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \) |
$1$ |
$4.351116790$ |
3.552671983 |
\( \frac{85184}{3} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -2 a + 2\) , \( -a + 1\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(-2a+2\right){x}-a+1$ |
| 75.1-b4 |
75.1-b |
$4$ |
$10$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.1 |
\( 3 \cdot 5^{2} \) |
\( 3^{10} \cdot 5^{6} \) |
$1.28828$ |
$(3,a), (5,a+2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 5$ |
2B, 5B |
$1$ |
\( 2^{3} \cdot 5 \) |
$1$ |
$0.870223358$ |
3.552671983 |
\( \frac{58591911104}{243} \) |
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -162 a + 82\) , \( 594 a - 3109\bigr] \) |
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(-162a+82\right){x}+594a-3109$ |
| 75.2-a1 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{32} \cdot 5^{2} \) |
$1.28828$ |
$(3,a), (5,a+2), (5,a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$5.298196352$ |
$0.558925428$ |
1.208944300 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$ |
| 75.2-a2 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{2} \cdot 5^{2} \) |
$1.28828$ |
$(3,a), (5,a+2), (5,a+3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1.324549088$ |
$8.942806850$ |
1.208944300 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2$ |
| 75.2-a3 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{16} \) |
$1.28828$ |
$(3,a), (5,a+2), (5,a+3)$ |
$1$ |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$0.662274544$ |
$1.117850856$ |
1.208944300 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$ |
| 75.2-a4 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{8} \cdot 5^{8} \) |
$1.28828$ |
$(3,a), (5,a+2), (5,a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \) |
$1.324549088$ |
$2.235701712$ |
1.208944300 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
| 75.2-a5 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{4} \cdot 5^{4} \) |
$1.28828$ |
$(3,a), (5,a+2), (5,a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.649098176$ |
$4.471403425$ |
1.208944300 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
| 75.2-a6 |
75.2-a |
$8$ |
$16$ |
\(\Q(\sqrt{-6}) \) |
$2$ |
$[0, 1]$ |
75.2 |
\( 3 \cdot 5^{2} \) |
\( 3^{16} \cdot 5^{4} \) |
$1.28828$ |
$(3,a), (5,a+2), (5,a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$2.649098176$ |
$1.117850856$ |
1.208944300 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$ |
*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.
