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
625.3-CMb1
625.3-CMb
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
625.3
\( 5^{4} \)
\( 5^{15} \)
$0.89359$
$(-a-2), (2a+1)$
0
$\Z/2\Z$
$\textsf{yes}$
$-4$
$\mathrm{U}(1)$
✓
✓
$5$
5Cs.1.3
$1$
\( 2^{2} \)
$1$
$1.839085544$
1.839085544
\( 1728 \)
\( \bigl[i + 1\) , \( i\) , \( 1\) , \( -13 i + 5\) , \( 3 i + 6\bigr] \)
${y}^2+\left(i+1\right){x}{y}+{y}={x}^{3}+i{x}^{2}+\left(-13i+5\right){x}+3i+6$
625.3-CMa1
625.3-CMa
$1$
$1$
\(\Q(\sqrt{-1}) \)
$2$
$[0, 1]$
625.3
\( 5^{4} \)
\( 5^{15} \)
$0.89359$
$(-a-2), (2a+1)$
0
$\Z/2\Z$
$\textsf{yes}$
$-4$
$\mathrm{U}(1)$
✓
✓
$5$
5Cs.1.3
$1$
\( 2^{2} \)
$1$
$1.839085544$
1.839085544
\( 1728 \)
\( \bigl[i + 1\) , \( i\) , \( i\) , \( 12 i + 6\) , \( 3 i - 6\bigr] \)
${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(12i+6\right){x}+3i-6$
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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.