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
593.1-a1
593.1-a
$2$
$2$
\(\Q(\sqrt{-163}) \)
$2$
$[0, 1]$
593.1
\( 593 \)
\( 593 \)
$5.62984$
$(a+23)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$9$
\( 1 \)
$1$
$8.223475941$
2.898505559
\( \frac{3503}{593} a - \frac{8168}{593} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 46\) , \( -3 a - 14\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+46{x}-3a-14$
593.1-a2
593.1-a
$2$
$2$
\(\Q(\sqrt{-163}) \)
$2$
$[0, 1]$
593.1
\( 593 \)
\( 593^{2} \)
$5.62984$
$(a+23)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$2$
2B
$9$
\( 2 \)
$1$
$4.111737970$
2.898505559
\( -\frac{672292257}{351649} a + \frac{6439664009}{351649} \)
\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 51\) , \( -4 a - 29\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a+1\right){x}^2+51{x}-4a-29$
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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.