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
1458.1-g3
1458.1-g
$3$
$9$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
1458.1
\( 2 \cdot 3^{6} \)
\( 2^{6} \cdot 3^{6} \)
$1.56179$
$(a), (3)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3 \)
$1$
$9.557777544$
2.252789771
\( \frac{9261}{8} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}-1$
1458.1-k3
1458.1-k
$3$
$9$
\(\Q(\sqrt{2}) \)
$2$
$[2, 0]$
1458.1
\( 2 \cdot 3^{6} \)
\( 2^{6} \cdot 3^{18} \)
$1.56179$
$(a), (3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3 \)
$0.847819441$
$4.429865119$
1.770466107
\( \frac{9261}{8} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 12\) , \( 8\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+12{x}+8$
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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.