| 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 |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 5^{12} \cdot 11^{2} \) |
$4.18079$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$7.655751664$ |
$0.370308724$ |
0.882815197 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -195508\) , \( 33338522\bigr] \) |
${y}^2+a{y}={x}^3-{x}^2-195508{x}+33338522$ |
| 11.1-a2 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 5^{12} \cdot 11^{10} \) |
$4.18079$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$1.531150332$ |
$1.851543623$ |
0.882815197 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -258\) , \( 3022\bigr] \) |
${y}^2+a{y}={x}^3-{x}^2-258{x}+3022$ |
| 11.1-a3 |
11.1-a |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 5^{12} \cdot 11^{2} \) |
$4.18079$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$0.306230066$ |
$9.257718117$ |
0.882815197 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -8\) , \( 22\bigr] \) |
${y}^2+a{y}={x}^3-{x}^2-8{x}+22$ |
| 11.1-b1 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$4.18079$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$9$ |
\( 2 \) |
$1$ |
$0.370308724$ |
0.518912912 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -7820\) , \( -263580\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-7820{x}-263580$ |
| 11.1-b2 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$4.18079$ |
$(11,a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$9$ |
\( 2 \cdot 5 \) |
$1$ |
$1.851543623$ |
0.518912912 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -10\) , \( -20\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-10{x}-20$ |
| 11.1-b3 |
11.1-b |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$4.18079$ |
$(11,a)$ |
0 |
$\Z/5\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.1 |
$9$ |
\( 2 \) |
$1$ |
$9.257718117$ |
0.518912912 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{y}={x}^3-{x}^2$ |
| 11.1-c1 |
11.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 3^{12} \cdot 11^{2} \) |
$4.18079$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$25$ |
\( 2 \) |
$1$ |
$0.370308724$ |
1.441424755 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -70383\) , \( -7186994\bigr] \) |
${y}^2+a{y}={x}^3-70383{x}-7186994$ |
| 11.1-c2 |
11.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 3^{12} \cdot 11^{10} \) |
$4.18079$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1.851543623$ |
1.441424755 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -93\) , \( -584\bigr] \) |
${y}^2+a{y}={x}^3-93{x}-584$ |
| 11.1-c3 |
11.1-c |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 3^{12} \cdot 11^{2} \) |
$4.18079$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$9.257718117$ |
1.441424755 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 0\) , \( a\) , \( -3\) , \( 46\bigr] \) |
${y}^2+a{y}={x}^3-3{x}+46$ |
| 11.1-d1 |
11.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{14} \) |
$4.18079$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$22.07430201$ |
$0.370308724$ |
2.545475631 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -946260\) , \( -354609598\bigr] \) |
${y}^2+a{y}={x}^3+{x}^2-946260{x}-354609598$ |
| 11.1-d2 |
11.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{22} \) |
$4.18079$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$4.414860402$ |
$1.851543623$ |
2.545475631 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -1250\) , \( -31198\bigr] \) |
${y}^2+a{y}={x}^3+{x}^2-1250{x}-31198$ |
| 11.1-d3 |
11.1-d |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{14} \) |
$4.18079$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$0.882972080$ |
$9.257718117$ |
2.545475631 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -40\) , \( 262\bigr] \) |
${y}^2+a{y}={x}^3+{x}^2-40{x}+262$ |
| 11.1-e1 |
11.1-e |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 3^{12} \cdot 11^{2} \) |
$4.18079$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$75.96435851$ |
$0.370308724$ |
8.759752554 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -70383\) , \( 7187035\bigr] \) |
${y}^2+{y}={x}^3-70383{x}+7187035$ |
| 11.1-e2 |
11.1-e |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 3^{12} \cdot 11^{10} \) |
$4.18079$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$15.19287170$ |
$1.851543623$ |
8.759752554 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -93\) , \( 625\bigr] \) |
${y}^2+{y}={x}^3-93{x}+625$ |
| 11.1-e3 |
11.1-e |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 3^{12} \cdot 11^{2} \) |
$4.18079$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$3.038574340$ |
$9.257718117$ |
8.759752554 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 0\) , \( 1\) , \( -3\) , \( -5\bigr] \) |
${y}^2+{y}={x}^3-3{x}-5$ |
| 11.1-f1 |
11.1-f |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{14} \) |
$4.18079$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$25$ |
\( 2 \) |
$1$ |
$0.370308724$ |
1.441424755 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -946260\) , \( 354609639\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-946260{x}+354609639$ |
| 11.1-f2 |
11.1-f |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{22} \) |
$4.18079$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1.851543623$ |
1.441424755 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -1250\) , \( 31239\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-1250{x}+31239$ |
| 11.1-f3 |
11.1-f |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{14} \) |
$4.18079$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$1$ |
$9.257718117$ |
1.441424755 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -40\) , \( -221\bigr] \) |
${y}^2+{y}={x}^3-{x}^2-40{x}-221$ |
| 11.1-g1 |
11.1-g |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 5^{12} \cdot 11^{2} \) |
$4.18079$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.3 |
$25$ |
\( 2 \) |
$1$ |
$0.370308724$ |
1.441424755 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -195508\) , \( -33338481\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-195508{x}-33338481$ |
| 11.1-g2 |
11.1-g |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 5^{12} \cdot 11^{10} \) |
$4.18079$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.3 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1.851543623$ |
1.441424755 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -258\) , \( -2981\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-258{x}-2981$ |
| 11.1-g3 |
11.1-g |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 5^{12} \cdot 11^{2} \) |
$4.18079$ |
$(11,a)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.1.3 |
$1$ |
\( 2 \) |
$1$ |
$9.257718117$ |
1.441424755 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -8\) , \( 19\bigr] \) |
${y}^2+{y}={x}^3+{x}^2-8{x}+19$ |
| 11.1-h1 |
11.1-h |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$4.18079$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$131.8741668$ |
$0.370308724$ |
15.20693509 |
\( -\frac{52893159101157376}{11} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -7820\) , \( 263621\bigr] \) |
${y}^2+a{y}={x}^3+{x}^2-7820{x}+263621$ |
| 11.1-h2 |
11.1-h |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{10} \) |
$4.18079$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$26.37483336$ |
$1.851543623$ |
15.20693509 |
\( -\frac{122023936}{161051} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( -10\) , \( 61\bigr] \) |
${y}^2+a{y}={x}^3+{x}^2-10{x}+61$ |
| 11.1-h3 |
11.1-h |
$3$ |
$25$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
11.1 |
\( 11 \) |
\( 11^{2} \) |
$4.18079$ |
$(11,a)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$5$ |
5Cs.4.1 |
$1$ |
\( 2 \) |
$5.274966672$ |
$9.257718117$ |
15.20693509 |
\( -\frac{4096}{11} \) |
\( \bigl[0\) , \( 1\) , \( a\) , \( 0\) , \( 41\bigr] \) |
${y}^2+a{y}={x}^3+{x}^2+41$ |
| 15.1-a1 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{14} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$9.352879577$ |
$0.558925428$ |
3.255721336 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -2073\) , \( 140232\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-2073{x}+140232$ |
| 15.1-a2 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{14} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.338219894$ |
$8.942806850$ |
3.255721336 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 677\) , \( -2768\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+677{x}-2768$ |
| 15.1-a3 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{28} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$4.676439788$ |
$1.117850856$ |
3.255721336 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 1552\) , \( -9768\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+1552{x}-9768$ |
| 15.1-a4 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{20} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$2.338219894$ |
$2.235701712$ |
3.255721336 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 427\) , \( 1482\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+427{x}+1482$ |
| 15.1-a5 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1.169109947$ |
$4.471403425$ |
3.255721336 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( 552\) , \( -1518\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+552{x}-1518$ |
| 15.1-a6 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{16} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$4.676439788$ |
$1.117850856$ |
3.255721336 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -2698\) , \( 120232\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-2698{x}+120232$ |
| 15.1-a7 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{14} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$0.584554973$ |
$2.235701712$ |
3.255721336 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -1323\) , \( -9018\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-1323{x}-9018$ |
| 15.1-a8 |
15.1-a |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{14} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$9.352879577$ |
$0.558925428$ |
3.255721336 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -53323\) , \( 5587732\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3-{x}^2-53323{x}+5587732$ |
| 15.1-b1 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \) |
$4.51787$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$0.558925428$ |
0.696196569 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$ |
| 15.1-b2 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$4.51787$ |
$(3,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$1$ |
$8.942806850$ |
0.696196569 |
\( -\frac{1}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2$ |
| 15.1-b3 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{16} \) |
$4.51787$ |
$(3,a), (5,a)$ |
0 |
$\Z/8\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{5} \) |
$1$ |
$1.117850856$ |
0.696196569 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$ |
| 15.1-b4 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{8} \) |
$4.51787$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{4} \) |
$1$ |
$2.235701712$ |
0.696196569 |
\( \frac{111284641}{50625} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$ |
| 15.1-b5 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{4} \cdot 5^{4} \) |
$4.51787$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$4.471403425$ |
0.696196569 |
\( \frac{13997521}{225} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$ |
| 15.1-b6 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$4.51787$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{3} \) |
$1$ |
$1.117850856$ |
0.696196569 |
\( \frac{272223782641}{164025} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$ |
| 15.1-b7 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \) |
$4.51787$ |
$(3,a), (5,a)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$2.235701712$ |
0.696196569 |
\( \frac{56667352321}{15} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$ |
| 15.1-b8 |
15.1-b |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{8} \cdot 5^{2} \) |
$4.51787$ |
$(3,a), (5,a)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$16$ |
\( 2^{2} \) |
$1$ |
$0.558925428$ |
0.696196569 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) |
${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$ |
| 15.1-c1 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{44} \cdot 5^{2} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$2.454423445$ |
$0.558925428$ |
6.835044726 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -423\) , \( -11502\bigr] \) |
${y}^2+a{x}{y}={x}^3-423{x}-11502$ |
| 15.1-c2 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{14} \cdot 5^{2} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$2.454423445$ |
$8.942806850$ |
6.835044726 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 567\) , \( -2592\bigr] \) |
${y}^2+a{x}{y}={x}^3+567{x}-2592$ |
| 15.1-c3 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{16} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$9.817693780$ |
$1.117850856$ |
6.835044726 |
\( \frac{4733169839}{3515625} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 882\) , \( -8073\bigr] \) |
${y}^2+a{x}{y}={x}^3+882{x}-8073$ |
| 15.1-c4 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{20} \cdot 5^{8} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$2.454423445$ |
$2.235701712$ |
6.835044726 |
\( \frac{111284641}{50625} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 477\) , \( -1512\bigr] \) |
${y}^2+a{x}{y}={x}^3+477{x}-1512$ |
| 15.1-c5 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{16} \cdot 5^{4} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{3} \) |
$2.454423445$ |
$4.471403425$ |
6.835044726 |
\( \frac{13997521}{225} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( 522\) , \( -1863\bigr] \) |
${y}^2+a{x}{y}={x}^3+522{x}-1863$ |
| 15.1-c6 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{28} \cdot 5^{4} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$2$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{5} \) |
$2.454423445$ |
$1.117850856$ |
6.835044726 |
\( \frac{272223782641}{164025} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -648\) , \( -2187\bigr] \) |
${y}^2+a{x}{y}={x}^3-648{x}-2187$ |
| 15.1-c7 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{14} \cdot 5^{2} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$2.454423445$ |
$2.235701712$ |
6.835044726 |
\( \frac{56667352321}{15} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -153\) , \( 14742\bigr] \) |
${y}^2+a{x}{y}={x}^3-153{x}+14742$ |
| 15.1-c8 |
15.1-c |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{20} \cdot 5^{2} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{4} \) |
$2.454423445$ |
$0.558925428$ |
6.835044726 |
\( \frac{1114544804970241}{405} \) |
\( \bigl[a\) , \( 0\) , \( 0\) , \( -18873\) , \( -778572\bigr] \) |
${y}^2+a{x}{y}={x}^3-18873{x}-778572$ |
| 15.1-d1 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{32} \cdot 5^{2} \cdot 11^{12} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$4.497953220$ |
$0.558925428$ |
6.262919200 |
\( -\frac{147281603041}{215233605} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( -12690\) , \( -933792\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2-12690{x}-933792$ |
| 15.1-d2 |
15.1-d |
$8$ |
$16$ |
\(\Q(\sqrt{-165}) \) |
$2$ |
$[0, 1]$ |
15.1 |
\( 3 \cdot 5 \) |
\( 3^{2} \cdot 5^{2} \cdot 11^{12} \) |
$4.51787$ |
$(3,a), (5,a)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$4$ |
\( 2^{2} \) |
$4.497953220$ |
$8.942806850$ |
6.262919200 |
\( -\frac{1}{15} \) |
\( \bigl[a\) , \( 1\) , \( a\) , \( 620\) , \( -2092\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+620{x}-2092$ |
*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.
