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
196.1-e6
196.1-e
$6$
$18$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{18} \cdot 7^{4} \)
$2.52429$
$(a-4), (a+3), (2a+7), (-2a+9)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.1
$1$
\( 2^{2} \cdot 3^{4} \)
$1$
$7.027708105$
8.377584104
\( \frac{2251439055699625}{25088} \)
\( \bigl[1\) , \( -a\) , \( a\) , \( -32984692 a - 108022130\) , \( 200392463513 a + 656268729042\bigr] \)
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-32984692a-108022130\right){x}+200392463513a+656268729042$
196.1-h6
196.1-h
$6$
$18$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
196.1
\( 2^{2} \cdot 7^{2} \)
\( 2^{18} \cdot 7^{4} \)
$2.52429$
$(a-4), (a+3), (2a+7), (-2a+9)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3B.1.2
$9$
\( 2^{2} \)
$1$
$0.436190660$
0.519973779
\( \frac{2251439055699625}{25088} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$
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.