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
1458.4-b3
1458.4-b
$3$
$9$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
1458.4
\( 2 \cdot 3^{6} \)
\( 2^{6} \cdot 3^{18} \)
$1.56179$
$(a), (-a-1), (a-1)$
$1$
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3^{2} \)
$0.338560565$
$1.878378408$
1.798723678
\( \frac{9261}{8} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 12\) , \( 8\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+12{x}+8$
1458.4-e3
1458.4-e
$3$
$9$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
1458.4
\( 2 \cdot 3^{6} \)
\( 2^{6} \cdot 3^{6} \)
$1.56179$
$(a), (-a-1), (a-1)$
0
$\Z/3\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs.1.1
$1$
\( 2 \cdot 3 \)
$1$
$5.635135226$
2.656428221
\( \frac{9261}{8} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( 1\) , \( -1\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+{x}-1$
11664.4-e3
11664.4-e
$3$
$9$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
11664.4
\( 2^{4} \cdot 3^{6} \)
\( 2^{18} \cdot 3^{6} \)
$2.62661$
$(a), (-a-1), (a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs
$1$
\( 2^{2} \)
$0.231321420$
$2.817567613$
3.686932492
\( \frac{9261}{8} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( 6\) , \( -6\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+6{x}-6$
11664.4-n3
11664.4-n
$3$
$9$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
11664.4
\( 2^{4} \cdot 3^{6} \)
\( 2^{18} \cdot 3^{18} \)
$2.62661$
$(a), (-a-1), (a-1)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$3$
3Cs
$1$
\( 2^{2} \)
$0.847819441$
$0.939189204$
4.504342982
\( \frac{9261}{8} \)
\( \bigl[a\) , \( -1\) , \( 0\) , \( 48\) , \( 64\bigr] \)
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+48{x}+64$
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.