| 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 |
| 5202.2-b3 |
5202.2-b |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
5202.2 |
\( 2 \cdot 3^{2} \cdot 17^{2} \) |
\( 2 \cdot 3^{2} \cdot 17^{13} \) |
$1.51779$ |
$(a+1), (a+4), (a-4), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.578067282$ |
$0.509184076$ |
1.766055929 |
\( \frac{461275687224792005}{3495733423378566} a + \frac{140679328163848447}{1165244474459522} \) |
\( \bigl[1\) , \( i\) , \( 0\) , \( 54 i - 70\) , \( -141 i - 971\bigr] \) |
${y}^2+{x}{y}={x}^{3}+i{x}^{2}+\left(54i-70\right){x}-141i-971$ |
| 46818.2-e3 |
46818.2-e |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
46818.2 |
\( 2 \cdot 3^{4} \cdot 17^{2} \) |
\( 2 \cdot 3^{14} \cdot 17^{13} \) |
$2.62889$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.169728025$ |
2.715648406 |
\( \frac{461275687224792005}{3495733423378566} a + \frac{140679328163848447}{1165244474459522} \) |
\( \bigl[i\) , \( 1\) , \( 1\) , \( 484 i - 627\) , \( -3179 i - 25732\bigr] \) |
${y}^2+i{x}{y}+{y}={x}^{3}+{x}^{2}+\left(484i-627\right){x}-3179i-25732$ |
| 88434.2-g3 |
88434.2-g |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
88434.2 |
\( 2 \cdot 3^{2} \cdot 17^{3} \) |
\( 2 \cdot 3^{2} \cdot 17^{19} \) |
$3.08193$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{2} \) |
$1$ |
$0.123495278$ |
1.975924450 |
\( \frac{461275687224792005}{3495733423378566} a + \frac{140679328163848447}{1165244474459522} \) |
\( \bigl[i\) , \( -1\) , \( i\) , \( -250 i + 1477\) , \( 43615 i - 51490\bigr] \) |
${y}^2+i{x}{y}+i{y}={x}^{3}-{x}^{2}+\left(-250i+1477\right){x}+43615i-51490$ |
| 88434.3-i3 |
88434.3-i |
$4$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$2$ |
$[0, 1]$ |
88434.3 |
\( 2 \cdot 3^{2} \cdot 17^{3} \) |
\( 2 \cdot 3^{2} \cdot 17^{19} \) |
$3.08193$ |
$(a+1), (a+4), (a-4), (3)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$16$ |
\( 2^{4} \cdot 3 \) |
$1$ |
$0.123495278$ |
5.927773351 |
\( \frac{461275687224792005}{3495733423378566} a + \frac{140679328163848447}{1165244474459522} \) |
\( \bigl[i\) , \( i + 1\) , \( i + 1\) , \( -1365 i + 615\) , \( -55137 i - 37555\bigr] \) |
${y}^2+i{x}{y}+\left(i+1\right){y}={x}^{3}+\left(i+1\right){x}^{2}+\left(-1365i+615\right){x}-55137i-37555$ |
*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.
