| 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 |
| 20736.3-CMb1 |
20736.3-CMb |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{24} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-11$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$0.960968773$ |
0.579485973 |
\( -32768 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 96\) , \( 224 a - 112\bigr] \) |
${y}^2={x}^{3}+96{x}+224a-112$ |
| 20736.3-CMa1 |
20736.3-CMa |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{24} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{yes}$ |
$-11$ |
$\mathrm{U}(1)$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 1 \) |
$1$ |
$0.960968773$ |
0.579485973 |
\( -32768 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 96\) , \( -224 a + 112\bigr] \) |
${y}^2={x}^{3}+96{x}-224a+112$ |
| 20736.3-a1 |
20736.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{32} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.998409326$ |
$0.206103277$ |
1.985396094 |
\( \frac{102129622}{59049} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1113\) , \( 260 a - 130\bigr] \) |
${y}^2={x}^{3}+1113{x}+260a-130$ |
| 20736.3-a2 |
20736.3-a |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{22} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.499204663$ |
$0.412206555$ |
1.985396094 |
\( \frac{63253004}{243} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 753\) , \( -4780 a + 2390\bigr] \) |
${y}^2={x}^{3}+753{x}-4780a+2390$ |
| 20736.3-b1 |
20736.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{32} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.998409326$ |
$0.206103277$ |
1.985396094 |
\( \frac{102129622}{59049} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 1113\) , \( -260 a + 130\bigr] \) |
${y}^2={x}^{3}+1113{x}-260a+130$ |
| 20736.3-b2 |
20736.3-b |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{22} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.499204663$ |
$0.412206555$ |
1.985396094 |
\( \frac{63253004}{243} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 753\) , \( 4780 a - 2390\bigr] \) |
${y}^2={x}^{3}+753{x}+4780a-2390$ |
| 20736.3-c1 |
20736.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{18} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.508571683$ |
0.909702953 |
\( \frac{151552}{27} a + \frac{63488}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a - 30\) , \( 32 a - 53\bigr] \) |
${y}^2={x}^{3}+\left(12a-30\right){x}+32a-53$ |
| 20736.3-c2 |
20736.3-c |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{21} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.754285841$ |
0.909702953 |
\( -\frac{1688800}{729} a + \frac{3105712}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 57 a - 75\) , \( -220 a + 10\bigr] \) |
${y}^2={x}^{3}+\left(57a-75\right){x}-220a+10$ |
| 20736.3-d1 |
20736.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{20} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.640489933$ |
$0.509175951$ |
6.293088271 |
\( \frac{18321686}{729} a - \frac{567362}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9 a + 357\) , \( 1584 a - 1006\bigr] \) |
${y}^2={x}^{3}+\left(9a+357\right){x}+1584a-1006$ |
| 20736.3-d2 |
20736.3-d |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{16} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.160122483$ |
$1.018351902$ |
6.293088271 |
\( \frac{868}{27} a - \frac{856}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9 a - 3\) , \( 72 a + 2\bigr] \) |
${y}^2={x}^{3}+\left(9a-3\right){x}+72a+2$ |
| 20736.3-e1 |
20736.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{21} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$0.754285841$ |
0.909702953 |
\( \frac{1688800}{729} a + \frac{472304}{243} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -57 a - 18\) , \( 220 a - 210\bigr] \) |
${y}^2={x}^{3}+\left(-57a-18\right){x}+220a-210$ |
| 20736.3-e2 |
20736.3-e |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{18} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$1.508571683$ |
0.909702953 |
\( -\frac{151552}{27} a + \frac{71680}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -12 a - 18\) , \( -32 a - 21\bigr] \) |
${y}^2={x}^{3}+\left(-12a-18\right){x}-32a-21$ |
| 20736.3-f1 |
20736.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{6} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.278951960$ |
$2.439013115$ |
3.282216264 |
\( 2916 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9\) , \( -4 a + 2\bigr] \) |
${y}^2={x}^{3}+9{x}-4a+2$ |
| 20736.3-f2 |
20736.3-f |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{6} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.557903920$ |
$1.219506557$ |
3.282216264 |
\( 4293378 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 129\) , \( -340 a + 170\bigr] \) |
${y}^2={x}^{3}+129{x}-340a+170$ |
| 20736.3-g1 |
20736.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{27} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.730894364$ |
$0.243787759$ |
3.438350454 |
\( \frac{36911280956}{531441} a - \frac{66690858806}{531441} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 720 a - 1911\) , \( 16748 a - 27022\bigr] \) |
${y}^2={x}^{3}+\left(720a-1911\right){x}+16748a-27022$ |
| 20736.3-g2 |
20736.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{27} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.923577459$ |
$0.243787759$ |
3.438350454 |
\( -\frac{36911280956}{531441} a - \frac{9926525950}{177147} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -720 a - 1191\) , \( 16748 a + 10274\bigr] \) |
${y}^2={x}^{3}+\left(-720a-1191\right){x}+16748a+10274$ |
| 20736.3-g3 |
20736.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{24} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.461788729$ |
$0.487575518$ |
3.438350454 |
\( \frac{202612}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -111\) , \( 620 a - 310\bigr] \) |
${y}^2={x}^{3}-111{x}+620a-310$ |
| 20736.3-g4 |
20736.3-g |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{18} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.730894364$ |
$0.975151036$ |
3.438350454 |
\( \frac{194672}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 69\) , \( 116 a - 58\bigr] \) |
${y}^2={x}^{3}+69{x}+116a-58$ |
| 20736.3-h1 |
20736.3-h |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{27} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$2.923577459$ |
$0.243787759$ |
3.438350454 |
\( \frac{36911280956}{531441} a - \frac{66690858806}{531441} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 720 a - 1911\) , \( -16748 a + 27022\bigr] \) |
${y}^2={x}^{3}+\left(720a-1911\right){x}-16748a+27022$ |
| 20736.3-h2 |
20736.3-h |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{27} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.730894364$ |
$0.243787759$ |
3.438350454 |
\( -\frac{36911280956}{531441} a - \frac{9926525950}{177147} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -720 a - 1191\) , \( -16748 a - 10274\bigr] \) |
${y}^2={x}^{3}+\left(-720a-1191\right){x}-16748a-10274$ |
| 20736.3-h3 |
20736.3-h |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{24} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{6} \) |
$1.461788729$ |
$0.487575518$ |
3.438350454 |
\( \frac{202612}{729} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -111\) , \( -620 a + 310\bigr] \) |
${y}^2={x}^{3}-111{x}-620a+310$ |
| 20736.3-h4 |
20736.3-h |
$4$ |
$4$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{18} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.730894364$ |
$0.975151036$ |
3.438350454 |
\( \frac{194672}{27} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 69\) , \( -116 a + 58\bigr] \) |
${y}^2={x}^{3}+69{x}-116a+58$ |
| 20736.3-i1 |
20736.3-i |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{6} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.278951960$ |
$2.439013115$ |
3.282216264 |
\( 2916 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9\) , \( 4 a - 2\bigr] \) |
${y}^2={x}^{3}+9{x}+4a-2$ |
| 20736.3-i2 |
20736.3-i |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{6} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.557903920$ |
$1.219506557$ |
3.282216264 |
\( 4293378 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 129\) , \( 340 a - 170\bigr] \) |
${y}^2={x}^{3}+129{x}+340a-170$ |
| 20736.3-j1 |
20736.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$0.762761577$ |
$1.408164878$ |
5.181624730 |
\( 2916 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 9 a - 27\) , \( 16 a - 30\bigr] \) |
${y}^2={x}^{3}+\left(9a-27\right){x}+16a-30$ |
| 20736.3-j2 |
20736.3-j |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1.525523155$ |
$0.704082439$ |
5.181624730 |
\( 4293378 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 129 a - 387\) , \( 1360 a - 2550\bigr] \) |
${y}^2={x}^{3}+\left(129a-387\right){x}+1360a-2550$ |
| 20736.3-k1 |
20736.3-k |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{15} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$1.306461400$ |
1.575651734 |
\( \frac{1688800}{729} a + \frac{472304}{243} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 21 a - 15\) , \( -40 a - 10\bigr] \) |
${y}^2={x}^{3}+\left(21a-15\right){x}-40a-10$ |
| 20736.3-k2 |
20736.3-k |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.612922801$ |
1.575651734 |
\( -\frac{151552}{27} a + \frac{71680}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a\) , \( 2 a + 11\bigr] \) |
${y}^2={x}^{3}+6a{x}+2a+11$ |
| 20736.3-l1 |
20736.3-l |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{15} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{4} \) |
$1$ |
$1.306461400$ |
3.151303469 |
\( \frac{1688800}{729} a + \frac{472304}{243} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 21 a - 15\) , \( 40 a + 10\bigr] \) |
${y}^2={x}^{3}+\left(21a-15\right){x}+40a+10$ |
| 20736.3-l2 |
20736.3-l |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1$ |
$2.612922801$ |
3.151303469 |
\( -\frac{151552}{27} a + \frac{71680}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6 a\) , \( -2 a - 11\bigr] \) |
${y}^2={x}^{3}+6a{x}-2a-11$ |
| 20736.3-m1 |
20736.3-m |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{20} \cdot 3^{16} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{6} \) |
$0.160122483$ |
$1.018351902$ |
6.293088271 |
\( -\frac{868}{27} a + \frac{4}{9} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9 a + 6\) , \( -72 a + 74\bigr] \) |
${y}^2={x}^{3}+\left(-9a+6\right){x}-72a+74$ |
| 20736.3-m2 |
20736.3-m |
$2$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{22} \cdot 3^{20} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{5} \) |
$0.640489933$ |
$0.509175951$ |
6.293088271 |
\( -\frac{18321686}{729} a + \frac{5918108}{243} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -9 a + 366\) , \( -1584 a + 578\bigr] \) |
${y}^2={x}^{3}+\left(-9a+366\right){x}-1584a+578$ |
| 20736.3-n1 |
20736.3-n |
$6$ |
$18$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{28} \cdot 3^{22} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.327424221$ |
1.579553877 |
\( \frac{503358625}{78732} a - \frac{272306375}{39366} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -315 a - 255\) , \( -4060 a + 1022\bigr] \) |
${y}^2={x}^{3}+\left(-315a-255\right){x}-4060a+1022$ |
| 20736.3-n2 |
20736.3-n |
$6$ |
$18$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{28} \cdot 3^{22} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{5} \) |
$1$ |
$0.327424221$ |
1.579553877 |
\( -\frac{503358625}{78732} a - \frac{13751375}{26244} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 315 a - 570\) , \( -4060 a + 3038\bigr] \) |
${y}^2={x}^{3}+\left(315a-570\right){x}-4060a+3038$ |
| 20736.3-n3 |
20736.3-n |
$6$ |
$18$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{26} \cdot 3^{32} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.163712110$ |
1.579553877 |
\( \frac{29733328625}{774840978} a - \frac{63954794125}{129140163} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 315 a + 870\) , \( -14140 a + 29246\bigr] \) |
${y}^2={x}^{3}+\left(315a+870\right){x}-14140a+29246$ |
| 20736.3-n4 |
20736.3-n |
$6$ |
$18$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{26} \cdot 3^{32} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{6} \) |
$1$ |
$0.163712110$ |
1.579553877 |
\( -\frac{29733328625}{774840978} a - \frac{353995436125}{774840978} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -315 a + 1185\) , \( -14140 a - 15106\bigr] \) |
${y}^2={x}^{3}+\left(-315a+1185\right){x}-14140a-15106$ |
| 20736.3-n5 |
20736.3-n |
$6$ |
$18$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{36} \cdot 3^{18} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{5} \) |
$1$ |
$0.327424221$ |
1.579553877 |
\( \frac{3723875}{1728} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 465\) , \( -1036 a + 518\bigr] \) |
${y}^2={x}^{3}+465{x}-1036a+518$ |
| 20736.3-n6 |
20736.3-n |
$6$ |
$18$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{30} \cdot 3^{24} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3Cs |
$1$ |
\( 2^{6} \) |
$1$ |
$0.163712110$ |
1.579553877 |
\( \frac{8934171875}{5832} \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 6225\) , \( -113932 a + 56966\bigr] \) |
${y}^2={x}^{3}+6225{x}-113932a+56966$ |
| 20736.3-o1 |
20736.3-o |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.949171984$ |
1.778417621 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 2 a - 5\bigr] \) |
${y}^2={x}^{3}+2a-5$ |
| 20736.3-o2 |
20736.3-o |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.949171984$ |
1.778417621 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 2 a + 3\bigr] \) |
${y}^2={x}^{3}+2a+3$ |
| 20736.3-o3 |
20736.3-o |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.474585992$ |
1.778417621 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15 a + 45\) , \( 44 a + 66\bigr] \) |
${y}^2={x}^{3}+\left(-15a+45\right){x}+44a+66$ |
| 20736.3-o4 |
20736.3-o |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.474585992$ |
1.778417621 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15 a + 30\) , \( 44 a - 110\bigr] \) |
${y}^2={x}^{3}+\left(15a+30\right){x}+44a-110$ |
| 20736.3-p1 |
20736.3-p |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.949171984$ |
1.778417621 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -2 a + 5\bigr] \) |
${y}^2={x}^{3}-2a+5$ |
| 20736.3-p2 |
20736.3-p |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.949171984$ |
1.778417621 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -2 a - 3\bigr] \) |
${y}^2={x}^{3}-2a-3$ |
| 20736.3-p3 |
20736.3-p |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.474585992$ |
1.778417621 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15 a + 45\) , \( -44 a - 66\bigr] \) |
${y}^2={x}^{3}+\left(-15a+45\right){x}-44a-66$ |
| 20736.3-p4 |
20736.3-p |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{12} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
0 |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
|
|
✓ |
|
|
$1$ |
\( 2^{3} \) |
$1$ |
$1.474585992$ |
1.778417621 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 15 a + 30\) , \( -44 a + 110\bigr] \) |
${y}^2={x}^{3}+\left(15a+30\right){x}-44a+110$ |
| 20736.3-q1 |
20736.3-q |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{18} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$2.435435646$ |
$1.702705239$ |
5.001263993 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 27\bigr] \) |
${y}^2={x}^{3}+27$ |
| 20736.3-q2 |
20736.3-q |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{8} \cdot 3^{6} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-3$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.811811882$ |
$5.108115717$ |
5.001263993 |
\( 0 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -1\bigr] \) |
${y}^2={x}^{3}-1$ |
| 20736.3-q3 |
20736.3-q |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{6} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$1.623623764$ |
$2.554057858$ |
5.001263993 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -15\) , \( -22\bigr] \) |
${y}^2={x}^{3}-15{x}-22$ |
| 20736.3-q4 |
20736.3-q |
$4$ |
$6$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
20736.3 |
\( 2^{8} \cdot 3^{4} \) |
\( 2^{16} \cdot 3^{18} \) |
$3.55645$ |
$(-a), (a-1), (2)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{potential}$ |
$-12$ |
$N(\mathrm{U}(1))$ |
✓ |
✓ |
|
✓ |
|
|
$1$ |
\( 2^{2} \) |
$4.870871293$ |
$0.851352619$ |
5.001263993 |
\( 54000 \) |
\( \bigl[0\) , \( 0\) , \( 0\) , \( -135\) , \( 594\bigr] \) |
${y}^2={x}^{3}-135{x}+594$ |
*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.
