| 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 |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 13^{20} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$1$ |
$0.092658541$ |
1.482536669 |
\( -\frac{1194176823177063550520521}{9981249137747697615} a - \frac{9808903772919038614296}{665416609183179841} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( 8925 i + 9605\) , \( -254835 i + 518800\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(8925i+9605\right){x}-254835i+518800$ |
| 38025.5-a2 |
38025.5-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 13^{20} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{6} \) |
$1$ |
$0.092658541$ |
1.482536669 |
\( \frac{1194176823177063550520521}{9981249137747697615} a - \frac{9808903772919038614296}{665416609183179841} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -8925 i + 9605\) , \( 254835 i + 518800\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+\left(-8925i+9605\right){x}+254835i+518800$ |
| 38025.5-a3 |
38025.5-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 5^{32} \cdot 13^{2} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{8} \) |
$1$ |
$0.092658541$ |
1.482536669 |
\( -\frac{55150149867714721}{5950927734375} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -7930\) , \( 296725\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-7930{x}+296725$ |
| 38025.5-a4 |
38025.5-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 5^{4} \cdot 13^{16} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$0.185317083$ |
1.482536669 |
\( \frac{24487529386319}{183539412225} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( 605\) , \( 19750\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+605{x}+19750$ |
| 38025.5-a5 |
38025.5-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{32} \cdot 5^{2} \cdot 13^{2} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{4} \) |
$1$ |
$0.370634167$ |
1.482536669 |
\( \frac{1023887723039}{2798036865} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( 210\) , \( -2277\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+210{x}-2277$ |
| 38025.5-a6 |
38025.5-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{16} \cdot 5^{4} \cdot 13^{4} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{7} \) |
$1$ |
$0.741268334$ |
1.482536669 |
\( \frac{168288035761}{27720225} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -115\) , \( -392\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-115{x}-392$ |
| 38025.5-a7 |
38025.5-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 5^{8} \cdot 13^{8} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/4\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{10} \) |
$1$ |
$0.370634167$ |
1.482536669 |
\( \frac{15551989015681}{1445900625} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -520\) , \( 4225\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-520{x}+4225$ |
| 38025.5-a8 |
38025.5-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{8} \cdot 5^{2} \cdot 13^{2} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{2} \) |
$1$ |
$1.482536669$ |
1.482536669 |
\( \frac{147281603041}{5265} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -110\) , \( -435\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-110{x}-435$ |
| 38025.5-a9 |
38025.5-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{4} \cdot 5^{16} \cdot 13^{4} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/2\Z\oplus\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{9} \) |
$1$ |
$0.185317083$ |
1.482536669 |
\( \frac{59319456301170001}{594140625} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -8125\) , \( 282568\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-8125{x}+282568$ |
| 38025.5-a10 |
38025.5-a |
$10$ |
$16$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 5^{8} \cdot 13^{2} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$16$ |
\( 2^{4} \) |
$1$ |
$0.092658541$ |
1.482536669 |
\( \frac{242970740812818720001}{24375} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -130000\) , \( 18051943\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-130000{x}+18051943$ |
| 38025.5-b1 |
38025.5-b |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{6} \cdot 5^{14} \cdot 13^{2} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 3 \) |
$1$ |
$0.779030811$ |
2.337092433 |
\( -\frac{32278933504}{27421875} \) |
\( \bigl[0\) , \( -1\) , \( i\) , \( -66\) , \( 349\bigr] \) |
${y}^2+i{y}={x}^{3}-{x}^{2}-66{x}+349$ |
| 38025.5-c1 |
38025.5-c |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{14} \cdot 5^{2} \cdot 13^{6} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 7 \) |
$1$ |
$0.680358928$ |
4.762512499 |
\( -\frac{762549907456}{24024195} \) |
\( \bigl[0\) , \( 1\) , \( i\) , \( -190\) , \( -1101\bigr] \) |
${y}^2+i{y}={x}^{3}+{x}^{2}-190{x}-1101$ |
| 38025.5-d1 |
38025.5-d |
$1$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
38025.5 |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
\( 3^{2} \cdot 5^{2} \cdot 13^{2} \) |
$2.49566$ |
$(-a-2), (2a+1), (-3a-2), (2a+3), (3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
|
|
$1$ |
\( 1 \) |
$1$ |
$5.819237497$ |
5.819237497 |
\( -\frac{4096}{195} \) |
\( \bigl[0\) , \( -1\) , \( i\) , \( 0\) , \( 1\bigr] \) |
${y}^2+i{y}={x}^{3}-{x}^{2}+1$ |
*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.
