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
729.1-a1
729.1-a
$2$
$3$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
729.1
\( 3^{6} \)
\( 3^{6} \)
$2.27471$
$(a+3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.2
$1$
\( 1 \)
$1.096515940$
$6.389222357$
2.860140232
\( -3386880 a - 8296128 \)
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -2 a - 6\) , \( -3 a - 7\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-2a-6\right){x}-3a-7$
729.1-c1
729.1-c
$2$
$3$
\(\Q(\sqrt{6}) \)
$2$
$[2, 0]$
729.1
\( 3^{6} \)
\( 3^{6} \)
$2.27471$
$(a+3)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1
$1$
\( 1 \)
$3.289547821$
$19.16766707$
2.860140232
\( -3386880 a - 8296128 \)
\( \bigl[a\) , \( 0\) , \( a + 1\) , \( a - 6\) , \( 156 a - 385\bigr] \)
${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-6\right){x}+156a-385$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.