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
135.6-a1
135.6-a
$4$
$6$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
135.6
\( 3^{3} \cdot 5 \)
\( 3^{9} \cdot 5^{4} \)
$1.01023$
$(-a), (a-1), (a-2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2^{3} \cdot 3 \)
$1$
$2.983066162$
1.199237719
\( \frac{8044322507}{455625} a - \frac{6011135363}{455625} \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( 6 a - 5\) , \( -6 a - 9\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-5\right){x}-6a-9$
135.6-a2
135.6-a
$4$
$6$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
135.6
\( 3^{3} \cdot 5 \)
\( 3^{6} \cdot 5^{2} \)
$1.01023$
$(-a), (a-1), (a-2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \cdot 3 \)
$1$
$5.966132324$
1.199237719
\( -\frac{622427}{675} a + \frac{1187018}{675} \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( a\) , \( 0\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+a{x}$
135.6-a3
135.6-a
$4$
$6$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
135.6
\( 3^{3} \cdot 5 \)
\( 3^{11} \cdot 5^{12} \)
$1.01023$
$(-a), (a-1), (a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$1$
\( 2^{3} \)
$1$
$0.994355387$
1.199237719
\( \frac{952048109087}{2197265625} a + \frac{3554857312792}{2197265625} \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -24 a + 40\) , \( -25 a - 15\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-24a+40\right){x}-25a-15$
135.6-a4
135.6-a
$4$
$6$
\(\Q(\sqrt{-11}) \)
$2$
$[0, 1]$
135.6
\( 3^{3} \cdot 5 \)
\( 3^{10} \cdot 5^{6} \)
$1.01023$
$(-a), (a-1), (a-2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
$2, 3$
2B , 3B.1.2
$1$
\( 2^{2} \)
$1$
$1.988710774$
1.199237719
\( -\frac{1392404117}{46875} a + \frac{1960195103}{46875} \)
\( \bigl[a\) , \( a + 1\) , \( a\) , \( -14 a + 15\) , \( -10 a + 69\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-14a+15\right){x}-10a+69$
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.