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
225.1-g2
225.1-g
$2$
$5$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 2^{12} \cdot 3^{10} \cdot 5^{4} \)
$2.18884$
$(3,a+1), (3,a+2), (5,a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.4
$1$
\( 1 \)
$1.580108742$
$9.835591419$
4.914591842
\( \frac{20480}{243} \)
\( \bigl[0\) , \( -1\) , \( 0\) , \( 7\) , \( 27\bigr] \)
${y}^2={x}^{3}-{x}^{2}+7{x}+27$
225.1-j2
225.1-j
$2$
$5$
\(\Q(\sqrt{10}) \)
$2$
$[2, 0]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{10} \cdot 5^{4} \)
$2.18884$
$(3,a+1), (3,a+2), (5,a)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$5$
5B.1.1
$1$
\( 3 \cdot 5^{2} \)
$0.277060067$
$9.835591419$
2.585209067
\( \frac{20480}{243} \)
\( \bigl[0\) , \( 1\) , \( 1\) , \( 2\) , \( 4\bigr] \)
${y}^2+{y}={x}^{3}+{x}^{2}+2{x}+4$
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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.