| 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 |
| 4225.5-a1 |
4225.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4225.5 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{4} \cdot 13^{4} \) |
$1.44087$ |
$(-a-2), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.187757049$ |
$3.421514516$ |
1.284826939 |
\( \frac{6967871}{4225} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 4\) , \( 1\bigr] \) |
${y}^2+{x}{y}={x}^{3}+4{x}+1$ |
| 4225.5-a2 |
4225.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4225.5 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{2} \cdot 13^{2} \) |
$1.44087$ |
$(-a-2), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.375514098$ |
$6.843029032$ |
1.284826939 |
\( \frac{117649}{65} \) |
\( \bigl[i\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2+i{x}{y}={x}^{3}-{x}$ |
| 4225.5-a3 |
4225.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4225.5 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{5} \cdot 13^{5} \) |
$1.44087$ |
$(-a-2), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.375514098$ |
$1.710757258$ |
1.284826939 |
\( -\frac{3286146785281}{17850625} a + \frac{3802553381608}{17850625} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( -5 i + 44\) , \( 111 i + 23\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(-5i+44\right){x}+111i+23$ |
| 4225.5-a4 |
4225.5-a |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
4225.5 |
\( 5^{2} \cdot 13^{2} \) |
\( 5^{5} \cdot 13^{5} \) |
$1.44087$ |
$(-a-2), (2a+1), (-3a-2), (2a+3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$0.375514098$ |
$1.710757258$ |
1.284826939 |
\( \frac{3286146785281}{17850625} a + \frac{3802553381608}{17850625} \) |
\( \bigl[1\) , \( 0\) , \( 0\) , \( 5 i + 44\) , \( -111 i + 23\bigr] \) |
${y}^2+{x}{y}={x}^{3}+\left(5i+44\right){x}-111i+23$ |
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*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.
