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
529.3-a1
529.3-a
$2$
$2$
\(\Q(\sqrt{-10}) \)
$2$
$[0, 1]$
529.3
\( 23^{2} \)
\( 23^{6} \)
$2.71039$
$(23,a+17)$
0
$\Z/2\Z$
$\textsf{potential}$
$-8$
$N(\mathrm{U}(1))$
✓
✓
$5$
5Nn.1.1.1
$1$
\( 2^{2} \)
$1$
$2.646045189$
0.836752959
\( 8000 \)
\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 3 a - 3\) , \( -3 a + 16\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+\left(3a-3\right){x}-3a+16$
529.3-a2
529.3-a
$2$
$2$
\(\Q(\sqrt{-10}) \)
$2$
$[0, 1]$
529.3
\( 23^{2} \)
\( 2^{12} \cdot 23^{6} \)
$2.71039$
$(23,a+17)$
0
$\Z/2\Z$
$\textsf{potential}$
$-8$
$N(\mathrm{U}(1))$
✓
✓
$5$
5Nn.1.1.1
$1$
\( 2^{2} \)
$1$
$2.646045189$
0.836752959
\( 8000 \)
\( \bigl[0\) , \( -a\) , \( 0\) , \( 10 a - 25\) , \( 33 a + 24\bigr] \)
${y}^2={x}^3-a{x}^2+\left(10a-25\right){x}+33a+24$
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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.