| 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 |
| 81225.2-a1 |
81225.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
81225.2 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{10} \cdot 5^{2} \cdot 19^{4} \) |
$3.01711$ |
$(-a-2), (2a+1), (3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 5 \) |
$0.269654355$ |
$1.577532480$ |
2.126942524 |
\( \frac{756058031}{438615} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( 19\) , \( 0\bigr] \) |
${y}^2+i{x}{y}={x}^{3}+19{x}$ |
| 81225.2-a2 |
81225.2-a |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
81225.2 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{20} \cdot 5^{4} \cdot 19^{2} \) |
$3.01711$ |
$(-a-2), (2a+1), (3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 5 \) |
$0.134827177$ |
$0.788766240$ |
2.126942524 |
\( \frac{48587168449}{28048275} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -76\) , \( 19\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-76{x}+19$ |
| 81225.2-b1 |
81225.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
81225.2 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{2} \cdot 5^{6} \cdot 19^{4} \) |
$3.01711$ |
$(-a-2), (2a+1), (3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$2.101383662$ |
$1.959065350$ |
4.116747922 |
\( \frac{357911}{135375} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( 2\) , \( 17\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}+2{x}+17$ |
| 81225.2-b2 |
81225.2-b |
$2$ |
$2$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
81225.2 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{4} \cdot 5^{12} \cdot 19^{2} \) |
$3.01711$ |
$(-a-2), (2a+1), (3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$1.050691831$ |
$0.979532675$ |
4.116747922 |
\( \frac{90458382169}{2671875} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -93\) , \( 378\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-93{x}+378$ |
| 81225.2-c1 |
81225.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
81225.2 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{16} \cdot 5^{6} \cdot 19^{2} \) |
$3.01711$ |
$(-a-2), (2a+1), (3), (19)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \cdot 3^{2} \) |
$0.213379982$ |
$0.885163107$ |
6.799539173 |
\( \frac{1256216039}{15582375} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( 23\) , \( 176\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}+23{x}+176$ |
| 81225.2-c2 |
81225.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
81225.2 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{4} \cdot 5^{24} \cdot 19^{2} \) |
$3.01711$ |
$(-a-2), (2a+1), (3), (19)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.853519928$ |
$0.221290776$ |
6.799539173 |
\( \frac{209595169258201}{41748046875} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -1237\) , \( -13054\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-1237{x}-13054$ |
| 81225.2-c3 |
81225.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
81225.2 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{8} \cdot 5^{12} \cdot 19^{4} \) |
$3.01711$ |
$(-a-2), (2a+1), (3), (19)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{5} \cdot 3^{2} \) |
$0.426759964$ |
$0.442581553$ |
6.799539173 |
\( \frac{6189976379881}{456890625} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -382\) , \( 2849\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-382{x}+2849$ |
| 81225.2-c4 |
81225.2-c |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
81225.2 |
\( 3^{2} \cdot 5^{2} \cdot 19^{2} \) |
\( 3^{4} \cdot 5^{6} \cdot 19^{8} \) |
$3.01711$ |
$(-a-2), (2a+1), (3), (19)$ |
$1$ |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$4$ |
\( 2^{3} \cdot 3^{2} \) |
$0.853519928$ |
$0.221290776$ |
6.799539173 |
\( \frac{23977812996389881}{146611125} \) |
\( \bigl[i\) , \( -1\) , \( 0\) , \( -6007\) , \( 181724\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}^{2}-6007{x}+181724$ |
*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.
