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
523.1-a1
523.1-a
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
523.1
\( 523 \)
\( 523^{3} \)
$0.74016$
$(-26a+9)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1[2]
$1$
\( 3 \)
$1$
$2.284168151$
0.879176731
\( \frac{11489855124637}{143055667} a - \frac{6128833451203}{143055667} \)
\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 18 a - 22\) , \( -40 a + 39\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(18a-22\right){x}-40a+39$
523.1-a2
523.1-a
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
523.1
\( 523 \)
\( 523 \)
$0.74016$
$(-26a+9)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$3$
3B.1.1[2]
$1$
\( 1 \)
$1$
$6.852504454$
0.879176731
\( -\frac{19832319}{523} a + \frac{11332126}{523} \)
\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -2 a - 2\) , \( 1\bigr] \)
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a-2\right){x}+1$
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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.