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
6561.4-a1
6561.4-a
$1$
$1$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
6561.4
\( 3^{8} \)
\( 3^{18} \)
$2.66733$
$(-a), (a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 3 \)
$0.310013903$
$1.758868167$
1.972874066
\( -159744 a + 589824 \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -3 a - 45\) , \( 11 a + 116\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+\left(-3a-45\right){x}+11a+116$
6561.4-b1
6561.4-b
$1$
$1$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
6561.4
\( 3^{8} \)
\( 3^{18} \)
$2.66733$
$(-a), (a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$1$
\( 1 \)
$2.238116432$
$1.758868167$
4.747660042
\( -159744 a + 589824 \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( -27 a\) , \( 69 a - 76\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-27a{x}+69a-76$
6561.4-c1
6561.4-c
$2$
$3$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
6561.4
\( 3^{8} \)
\( 3^{14} \)
$2.66733$
$(-a), (a-1)$
$1$
$\mathsf{trivial}$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$3$
3B.1.2
$1$
\( 1 \)
$1.077867740$
$3.898221876$
5.067522399
\( 0 \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( 2\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}+2$
6561.4-c2
6561.4-c
$2$
$3$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
6561.4
\( 3^{8} \)
\( 3^{14} \)
$2.66733$
$(-a), (a-1)$
$1$
$\Z/3\Z$
$\textsf{potential}$
$-3$
$N(\mathrm{U}(1))$
✓
✓
$3$
3B.1.1
$1$
\( 3 \)
$3.233603220$
$3.898221876$
5.067522399
\( 0 \)
\( \bigl[0\) , \( 0\) , \( a + 1\) , \( 0\) , \( -2 a + 2\bigr] \)
${y}^2+\left(a+1\right){y}={x}^{3}-2a+2$
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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.