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
25.1-a1
25.1-a
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
25.1
\( 5^{2} \)
\( 5^{4} \)
$1.45466$
$(5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.147790867$
$25.86029770$
2.099922056
\( -\frac{373457}{25} a - \frac{1134461}{25} \)
\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -2 a - 5\) , \( a + 2\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2a-5\right){x}+a+2$
25.1-b1
25.1-b
$1$
$1$
\(\Q(\sqrt{53}) \)
$2$
$[2, 0]$
25.1
\( 5^{2} \)
\( 5^{4} \)
$1.45466$
$(5)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 2 \)
$0.147790867$
$25.86029770$
2.099922056
\( \frac{373457}{25} a - \frac{1507918}{25} \)
\( \bigl[1\) , \( 0\) , \( a\) , \( a - 6\) , \( -2 a + 4\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-6\right){x}-2a+4$
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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.