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-CMb1
729.1-CMb
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
729.1
\( 3^{6} \)
\( 3^{6} \)
$0.80423$
$(-2a+1)$
0
$\Z/3\Z$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 1 \)
$1$
$8.108628264$
1.040337491
\( 0 \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -a\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-a$
729.1-CMa1
729.1-CMa
$1$
$1$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
729.1
\( 3^{6} \)
\( 3^{6} \)
$0.80423$
$(-2a+1)$
0
$\Z/3\Z$
$\textsf{yes}$
$-3$
$\mathrm{U}(1)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 1 \)
$1$
$8.108628264$
1.040337491
\( 0 \)
\( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( 0\bigr] \)
${y}^2+a{y}={x}^{3}$
729.1-a1
729.1-a
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
729.1
\( 3^{6} \)
\( 3^{6} \)
$0.80423$
$(-2a+1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 1 \)
$1$
$6.976113039$
0.895035720
\( -18981 a + 13149 \)
\( \bigl[1\) , \( -1\) , \( a\) , \( -2 a\) , \( a\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}-2a{x}+a$
729.1-a2
729.1-a
$2$
$3$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
729.1
\( 3^{6} \)
\( 3^{6} \)
$0.80423$
$(-2a+1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3B.1.1[2]
$1$
\( 1 \)
$1$
$6.976113039$
0.895035720
\( 18981 a - 5832 \)
\( \bigl[1\) , \( -1\) , \( a + 1\) , \( a - 2\) , \( -2 a + 1\bigr] \)
${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(a-2\right){x}-2a+1$
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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.