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
4.1-c3
4.1-c
$4$
$10$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
4.1
\( 2^{2} \)
\( - 2^{33} \)
$1.82695$
$(11a+74), (11a-85)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3, 5$
2B , 3Nn , 5B
$1$
\( 2 \cdot 3^{2} \cdot 5 \)
$1$
$2.636252383$
4.102951284
\( \frac{24345866052441}{1073741824} a - \frac{46176275773215}{268435456} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -25 a - 171\) , \( 132 a + 887\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-25a-171\right){x}+132a+887$
4.1-d3
4.1-d
$4$
$10$
\(\Q(\sqrt{209}) \)
$2$
$[2, 0]$
4.1
\( 2^{2} \)
\( - 2^{33} \)
$1.82695$
$(11a+74), (11a-85)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3, 5$
2B , 3Nn , 5B
$1$
\( 2 \)
$1$
$8.606301134$
0.297655148
\( \frac{24345866052441}{1073741824} a - \frac{46176275773215}{268435456} \)
\( \bigl[1\) , \( -1\) , \( 0\) , \( 1485209680 a - 11478318473\) , \( -83988775088712 a + 649100205595989\bigr] \)
${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(1485209680a-11478318473\right){x}-83988775088712a+649100205595989$
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.