| 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 |
| 11.1-a1 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$1.52661$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$4$ |
\( 2 \) |
$1$ |
$0.370308724$ |
0.631600683 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$ |
| 11.1-a2 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$1.52661$ |
$(11,a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$4$ |
\( 2 \cdot 5 \) |
$1$ |
$1.851543623$ |
0.631600683 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-10{x}-20$ |
| 11.1-a3 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$1.52661$ |
$(11,a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$4$ |
\( 2 \) |
$1$ |
$9.257718117$ |
0.631600683 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3-{x}^2$ |
| 11.1-b1 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 2^{12} \cdot 11^{2} \) |
$1.52661$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$12.68007523$ |
$0.370308724$ |
4.004372090 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -31281\) , \( -2139919\bigr] \) |
${y}^2={x}^3+{x}^2-31281{x}-2139919$ |
| 11.1-b2 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 2^{12} \cdot 11^{10} \) |
$1.52661$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$2.536015047$ |
$1.851543623$ |
4.004372090 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -199\bigr] \) |
${y}^2={x}^3+{x}^2-41{x}-199$ |
| 11.1-b3 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 2^{12} \cdot 11^{2} \) |
$1.52661$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$0.507203009$ |
$9.257718117$ |
4.004372090 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 1\bigr] \) |
${y}^2={x}^3+{x}^2-{x}+1$ |
| 32.1-a1 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$1.99373$ |
$(2,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.732897270 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 0\bigr] \) |
${y}^2={x}^3-4{x}$ |
| 32.1-a2 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$1.99373$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.732897270 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3+{x}$ |
| 32.1-a3 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$1.99373$ |
$(2,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$4$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.732897270 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 15\) , \( 8\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+15{x}+8$ |
| 32.1-a4 |
32.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{6} \) |
$1.99373$ |
$(2,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2 \) |
$1$ |
$6.875185818$ |
0.732897270 |
\( 287496 \) |
\( \bigl[a\) , \( 1\) , \( 0\) , \( 4\) , \( -1\bigr] \) |
${y}^2+a{x}{y}={x}^3+{x}^2+4{x}-1$ |
| 32.1-b1 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{12} \) |
$1.99373$ |
$(2,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$4.253144970$ |
$6.875185818$ |
3.117118340 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}$ |
| 32.1-b2 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{24} \) |
$1.99373$ |
$(2,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-4$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$8.506289940$ |
$6.875185818$ |
3.117118340 |
\( 1728 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 4\) , \( 0\bigr] \) |
${y}^2={x}^3+4{x}$ |
| 32.1-b3 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$1.99373$ |
$(2,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$2.126572485$ |
$6.875185818$ |
3.117118340 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( -14\bigr] \) |
${y}^2={x}^3-11{x}-14$ |
| 32.1-b4 |
32.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
32.1 |
\( 2^{5} \) |
\( 2^{18} \) |
$1.99373$ |
$(2,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{potential}$ |
$-16$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2Cs |
$1$ |
\( 2 \) |
$8.506289940$ |
$6.875185818$ |
3.117118340 |
\( 287496 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -11\) , \( 14\bigr] \) |
${y}^2={x}^3-11{x}+14$ |
| 44.1-a1 |
44.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{16} \cdot 11^{6} \) |
$2.15895$ |
$(2,a), (11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \) |
$1$ |
$2.457445862$ |
1.047858436 |
\( -\frac{199794688}{1331} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -77\) , \( -289\bigr] \) |
${y}^2={x}^3+{x}^2-77{x}-289$ |
| 44.1-a2 |
44.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{16} \cdot 11^{2} \) |
$2.15895$ |
$(2,a), (11,a)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B.1.1 |
$1$ |
\( 2 \cdot 3 \) |
$1$ |
$7.372337588$ |
1.047858436 |
\( \frac{8192}{11} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( -1\bigr] \) |
${y}^2={x}^3+{x}^2+3{x}-1$ |
| 44.1-b1 |
44.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11^{6} \) |
$2.15895$ |
$(2,a), (11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2 \cdot 3^{2} \) |
$0.172006545$ |
$2.457445862$ |
3.244293182 |
\( -\frac{199794688}{1331} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -19\) , \( -21\bigr] \) |
${y}^2+a{y}={x}^3-{x}^2-19{x}-21$ |
| 44.1-b2 |
44.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
44.1 |
\( 2^{2} \cdot 11 \) |
\( 2^{4} \cdot 11^{2} \) |
$2.15895$ |
$(2,a), (11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$3$ |
3B |
$1$ |
\( 2 \) |
$0.516019637$ |
$7.372337588$ |
3.244293182 |
\( \frac{8192}{11} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( 1\) , \( 5\bigr] \) |
${y}^2+a{y}={x}^3-{x}^2+{x}+5$ |
| 72.1-a1 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{16} \) |
$2.44182$ |
$(2,a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$1$ |
$1.817673508$ |
1.550117176 |
\( \frac{207646}{6561} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 29\) , \( -35\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+29{x}-35$ |
| 72.1-a2 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$2.44182$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
1.550117176 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 3\bigr] \) |
${y}^2={x}^3+{x}^2+3{x}+3$ |
| 72.1-a3 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{4} \cdot 3^{4} \) |
$2.44182$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$7.270694035$ |
1.550117176 |
\( \frac{35152}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 24\) , \( -2\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+24{x}-2$ |
| 72.1-a4 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{8} \) |
$2.44182$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$1$ |
$3.635347017$ |
1.550117176 |
\( \frac{1556068}{81} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 19\) , \( 3\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+19{x}+3$ |
| 72.1-a5 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.44182$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2 \) |
$1$ |
$3.635347017$ |
1.550117176 |
\( \frac{28756228}{3} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 9\) , \( 55\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+9{x}+55$ |
| 72.1-a6 |
72.1-a |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{10} \cdot 3^{4} \) |
$2.44182$ |
$(2,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$1.817673508$ |
1.550117176 |
\( \frac{3065617154}{9} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -71\) , \( -159\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-71{x}-159$ |
| 72.1-b1 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{16} \) |
$2.44182$ |
$(2,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1.251085853$ |
$1.817673508$ |
3.878659341 |
\( \frac{207646}{6561} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 16\) , \( -180\bigr] \) |
${y}^2={x}^3-{x}^2+16{x}-180$ |
| 72.1-b2 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{8} \cdot 3^{2} \) |
$2.44182$ |
$(2,a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$10.00868682$ |
$7.270694035$ |
3.878659341 |
\( \frac{2048}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) |
${y}^2={x}^3-{x}^2+{x}$ |
| 72.1-b3 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{16} \cdot 3^{4} \) |
$2.44182$ |
$(2,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$5.004343412$ |
$7.270694035$ |
3.878659341 |
\( \frac{35152}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 4\bigr] \) |
${y}^2={x}^3-{x}^2-4{x}+4$ |
| 72.1-b4 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{8} \) |
$2.44182$ |
$(2,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$2.502171706$ |
$3.635347017$ |
3.878659341 |
\( \frac{1556068}{81} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -24\) , \( -36\bigr] \) |
${y}^2={x}^3-{x}^2-24{x}-36$ |
| 72.1-b5 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{20} \cdot 3^{2} \) |
$2.44182$ |
$(2,a), (3)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$10.00868682$ |
$3.635347017$ |
3.878659341 |
\( \frac{28756228}{3} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -64\) , \( 220\bigr] \) |
${y}^2={x}^3-{x}^2-64{x}+220$ |
| 72.1-b6 |
72.1-b |
$6$ |
$8$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
72.1 |
\( 2^{3} \cdot 3^{2} \) |
\( 2^{22} \cdot 3^{4} \) |
$2.44182$ |
$(2,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$5.004343412$ |
$1.817673508$ |
3.878659341 |
\( \frac{3065617154}{9} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( -384\) , \( -2772\bigr] \) |
${y}^2={x}^3-{x}^2-384{x}-2772$ |
| 88.1-a1 |
88.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
88.1 |
\( 2^{3} \cdot 11 \) |
\( 2^{16} \cdot 11^{2} \) |
$2.56744$ |
$(2,a), (11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$9$ |
\( 2^{2} \) |
$0.040264364$ |
$7.039737974$ |
4.351094320 |
\( -\frac{27648}{11} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 4\bigr] \) |
${y}^2={x}^3-4{x}+4$ |
| 88.1-b1 |
88.1-b |
$1$ |
$1$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
88.1 |
\( 2^{3} \cdot 11 \) |
\( 2^{4} \cdot 11^{2} \) |
$2.56744$ |
$(2,a), (11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
|
|
$1$ |
\( 2^{2} \) |
$0.360248450$ |
$7.039737974$ |
4.325509429 |
\( -\frac{27648}{11} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -1\) , \( 6\bigr] \) |
${y}^2+a{y}={x}^3-{x}+6$ |
| 98.1-a1 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{36} \cdot 7^{2} \) |
$2.63746$ |
$(2,a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2 \) |
$1$ |
$0.875417135$ |
0.373279120 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-171{x}-874$ |
| 98.1-a2 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{4} \cdot 7^{2} \) |
$2.63746$ |
$(2,a), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2 \) |
$1$ |
$7.878754216$ |
0.373279120 |
\( -\frac{15625}{28} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-{x}$ |
| 98.1-a3 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{12} \cdot 7^{6} \) |
$2.63746$ |
$(2,a), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$2.626251405$ |
0.373279120 |
\( \frac{9938375}{21952} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+4{x}-6$ |
| 98.1-a4 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{6} \cdot 7^{12} \) |
$2.63746$ |
$(2,a), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$1.313125702$ |
0.373279120 |
\( \frac{4956477625}{941192} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-36{x}-70$ |
| 98.1-a5 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{2} \cdot 7^{4} \) |
$2.63746$ |
$(2,a), (7)$ |
0 |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$3.939377108$ |
0.373279120 |
\( \frac{128787625}{98} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-11{x}+12$ |
| 98.1-a6 |
98.1-a |
$6$ |
$18$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{4} \) |
$2.63746$ |
$(2,a), (7)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs.1.1 |
$4$ |
\( 2^{2} \) |
$1$ |
$0.437708567$ |
0.373279120 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3-2731{x}-55146$ |
| 98.1-b1 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{48} \cdot 7^{2} \) |
$2.63746$ |
$(2,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$9$ |
\( 2^{2} \cdot 3^{2} \) |
$0.210429933$ |
$0.875417135$ |
6.362477156 |
\( -\frac{548347731625}{1835008} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -672\) , \( -5632\bigr] \) |
${y}^2+a{x}{y}={x}^3-672{x}-5632$ |
| 98.1-b2 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{16} \cdot 7^{2} \) |
$2.63746$ |
$(2,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$1.893869405$ |
$7.878754216$ |
6.362477156 |
\( -\frac{15625}{28} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 8\) , \( 0\bigr] \) |
${y}^2+a{x}{y}={x}^3+8{x}$ |
| 98.1-b3 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{24} \cdot 7^{6} \) |
$2.63746$ |
$(2,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.631289801$ |
$2.626251405$ |
6.362477156 |
\( \frac{9938375}{21952} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 28\) , \( -88\bigr] \) |
${y}^2+a{x}{y}={x}^3+28{x}-88$ |
| 98.1-b4 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{18} \cdot 7^{12} \) |
$2.63746$ |
$(2,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$1.262579603$ |
$1.313125702$ |
6.362477156 |
\( \frac{4956477625}{941192} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -132\) , \( -280\bigr] \) |
${y}^2+a{x}{y}={x}^3-132{x}-280$ |
| 98.1-b5 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{14} \cdot 7^{4} \) |
$2.63746$ |
$(2,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{2} \) |
$3.787738810$ |
$3.939377108$ |
6.362477156 |
\( \frac{128787625}{98} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -32\) , \( 176\bigr] \) |
${y}^2+a{x}{y}={x}^3-32{x}+176$ |
| 98.1-b6 |
98.1-b |
$6$ |
$18$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
98.1 |
\( 2 \cdot 7^{2} \) |
\( 2^{30} \cdot 7^{4} \) |
$2.63746$ |
$(2,a), (7)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3Cs |
$9$ |
\( 2^{2} \cdot 3^{2} \) |
$0.420859867$ |
$0.437708567$ |
6.362477156 |
\( \frac{2251439055699625}{25088} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -10912\) , \( -419328\bigr] \) |
${y}^2+a{x}{y}={x}^3-10912{x}-419328$ |
| 99.1-a1 |
99.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 2^{12} \cdot 3^{24} \cdot 11^{2} \) |
$2.64417$ |
$(11,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$1.025585977$ |
1.311933990 |
\( \frac{9090072503}{5845851} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 199\) , \( -87\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+199{x}-87$ |
| 99.1-a2 |
99.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 2^{12} \cdot 3^{12} \cdot 11^{4} \) |
$2.64417$ |
$(11,a), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \cdot 3 \) |
$1$ |
$2.051171954$ |
1.311933990 |
\( \frac{169112377}{88209} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -21\) , \( 133\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-21{x}+133$ |
| 99.1-a3 |
99.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 2^{12} \cdot 3^{6} \cdot 11^{2} \) |
$2.64417$ |
$(11,a), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$4.102343908$ |
1.311933990 |
\( \frac{30664297}{297} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -1\) , \( 1\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-{x}+1$ |
| 99.1-a4 |
99.1-a |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 2^{12} \cdot 3^{6} \cdot 11^{8} \) |
$2.64417$ |
$(11,a), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2 \cdot 3 \) |
$1$ |
$1.025585977$ |
1.311933990 |
\( \frac{347873904937}{395307} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -561\) , \( 6721\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-561{x}+6721$ |
| 99.1-b1 |
99.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{24} \cdot 11^{2} \) |
$2.64417$ |
$(11,a), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$1.818439634$ |
$1.025585977$ |
4.771345529 |
\( \frac{9090072503}{5845851} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2+44{x}+55$ |
| 99.1-b2 |
99.1-b |
$4$ |
$4$ |
\(\Q(\sqrt{-22}) \) |
$2$ |
$[0, 1]$ |
99.1 |
\( 3^{2} \cdot 11 \) |
\( 3^{12} \cdot 11^{4} \) |
$2.64417$ |
$(11,a), (3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \cdot 3 \) |
$3.636879268$ |
$2.051171954$ |
4.771345529 |
\( \frac{169112377}{88209} \) |
\( \bigl[1\) , \( 1\) , \( 0\) , \( -11\) , \( 0\bigr] \) |
${y}^2+{x}{y}={x}^3+{x}^2-11{x}$ |
*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.
