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
5625.2-a2
5625.2-a
$2$
$5$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
5625.2
\( 3^{2} \cdot 5^{4} \)
\( 3^{10} \cdot 5^{4} \)
$2.18884$
$(-a-1), (a-1), (5)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.1
$1$
\( 5^{2} \)
$0.571930173$
$3.274603091$
2.648601831
\( \frac{20480}{243} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 2\) , \( 4\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+2{x}+4$
5625.2-c2
5625.2-c
$2$
$5$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
5625.2
\( 3^{2} \cdot 5^{4} \)
\( 3^{10} \cdot 5^{16} \)
$2.18884$
$(-a-1), (a-1), (5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.4
$1$
\( 3 \)
$1.809175777$
$0.654920618$
5.026962901
\( \frac{20480}{243} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 42\) , \( 443\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}+42{x}+443$
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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.