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-a1
225.1-a
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{10} \cdot 5^{4} \)
$0.97888$
$(-a-1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.924763210$
2.068119899
\( \frac{13634816}{2025} a - \frac{1569728}{2025} \)
\( \bigl[a\) , \( -1\) , \( 1\) , \( -3 a + 8\) , \( -4 a - 9\bigr] \)
${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-3a+8\right){x}-4a-9$
225.1-a2
225.1-a
$2$
$2$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
225.1
\( 3^{2} \cdot 5^{2} \)
\( 3^{14} \cdot 5^{2} \)
$0.97888$
$(-a-1), (5)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2$
2B
$1$
\( 2^{2} \)
$1$
$2.924763210$
2.068119899
\( -\frac{5468416}{32805} a - \frac{12586688}{32805} \)
\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 2 a + 2\) , \( 5\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(2a+2\right){x}+5$
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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.