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 |
38025.5-a1 |
38025.5-a |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{14} \cdot 5^{2} \cdot 13^{6} \) |
$4.13859$ |
$(-a), (a-1), (-a-1), (a-2), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 3 \) |
$1$ |
$0.680358928$ |
1.230815611 |
\( -\frac{762549907456}{24024195} \) |
\( \bigl[0\) , \( -1\) , \( 1\) , \( -190\) , \( 1101\bigr] \) |
${y}^2+{y}={x}^{3}-{x}^{2}-190{x}+1101$ |
38025.5-b1 |
38025.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 5^{32} \cdot 13^{2} \) |
$4.13859$ |
$(-a), (a-1), (-a-1), (a-2), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.092658541$ |
3.576012997 |
\( -\frac{55150149867714721}{5950927734375} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -7930\) , \( -296725\bigr] \) |
${y}^2+{x}{y}={x}^{3}-7930{x}-296725$ |
38025.5-b2 |
38025.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 5^{4} \cdot 13^{16} \) |
$4.13859$ |
$(-a), (a-1), (-a-1), (a-2), (13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{7} \) |
$1$ |
$0.185317083$ |
3.576012997 |
\( \frac{24487529386319}{183539412225} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 605\) , \( -19750\bigr] \) |
${y}^2+{x}{y}={x}^{3}+605{x}-19750$ |
38025.5-b3 |
38025.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{32} \cdot 5^{2} \cdot 13^{2} \) |
$4.13859$ |
$(-a), (a-1), (-a-1), (a-2), (13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.370634167$ |
3.576012997 |
\( \frac{1023887723039}{2798036865} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 210\) , \( 2277\bigr] \) |
${y}^2+{x}{y}={x}^{3}+210{x}+2277$ |
38025.5-b4 |
38025.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{16} \cdot 5^{4} \cdot 13^{4} \) |
$4.13859$ |
$(-a), (a-1), (-a-1), (a-2), (13)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$0.741268334$ |
3.576012997 |
\( \frac{168288035761}{27720225} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -115\) , \( 392\bigr] \) |
${y}^2+{x}{y}={x}^{3}-115{x}+392$ |
38025.5-b5 |
38025.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 5^{8} \cdot 13^{8} \) |
$4.13859$ |
$(-a), (a-1), (-a-1), (a-2), (13)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$0.370634167$ |
3.576012997 |
\( \frac{15551989015681}{1445900625} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -520\) , \( -4225\bigr] \) |
${y}^2+{x}{y}={x}^{3}-520{x}-4225$ |
38025.5-b6 |
38025.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 13^{2} \) |
$4.13859$ |
$(-a), (a-1), (-a-1), (a-2), (13)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$1.482536669$ |
3.576012997 |
\( \frac{147281603041}{5265} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -110\) , \( 435\bigr] \) |
${y}^2+{x}{y}={x}^{3}-110{x}+435$ |
38025.5-b7 |
38025.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 5^{16} \cdot 13^{4} \) |
$4.13859$ |
$(-a), (a-1), (-a-1), (a-2), (13)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$0.185317083$ |
3.576012997 |
\( \frac{59319456301170001}{594140625} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -8125\) , \( -282568\bigr] \) |
${y}^2+{x}{y}={x}^{3}-8125{x}-282568$ |
38025.5-b8 |
38025.5-b |
$8$ |
$16$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 5^{8} \cdot 13^{2} \) |
$4.13859$ |
$(-a), (a-1), (-a-1), (a-2), (13)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.092658541$ |
3.576012997 |
\( \frac{242970740812818720001}{24375} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -130000\) , \( -18051943\bigr] \) |
${y}^2+{x}{y}={x}^{3}-130000{x}-18051943$ |
38025.5-c1 |
38025.5-c |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 5^{14} \cdot 13^{2} \) |
$4.13859$ |
$(-a), (a-1), (-a-1), (a-2), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 3^{2} \) |
$1$ |
$0.779030811$ |
4.227959292 |
\( -\frac{32278933504}{27421875} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -66\) , \( -349\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-66{x}-349$ |
38025.5-d1 |
38025.5-d |
$1$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
$4.13859$ |
$(-a), (a-1), (-a-1), (a-2), (13)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$5.819237497$ |
3.509132244 |
\( -\frac{4096}{195} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 0\) , \( -1\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-1$ |
*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.