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
121.1-a3
121.1-a
$3$
$25$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$2.23755$
$(11)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.4.1
$1$
\( 1 \)
$5.612837583$
$8.512583687$
12.65716488
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -4027 a - 13182\) , \( -646194 a - 2116235\bigr] \)
${y}^2+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-4027a-13182\right){x}-646194a-2116235$
121.1-d3
121.1-d
$3$
$25$
\(\Q(\sqrt{57}) \)
$2$
$[2, 0]$
121.1
\( 11^{2} \)
\( 11^{2} \)
$2.23755$
$(11)$
$1$
$\Z/5\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$5$
5B.1.1
$1$
\( 1 \)
$0.964772481$
$40.27230645$
0.411702941
\( -\frac{4096}{11} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}$
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.