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
171.1-e1
171.1-e
$1$
$1$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
171.1
\( 3^{2} \cdot 19 \)
\( 3^{4} \cdot 19^{2} \)
$2.81705$
$(-a-4), (-a+4), (a)$
$2$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$1$
\( 2^{3} \)
$0.014286018$
$30.86363048$
1.618457864
\( -\frac{1404928}{171} \)
\( \bigl[0\) , \( -1\) , \( 1\) , \( -2\) , \( 2\bigr] \)
${y}^2+{y}={x}^{3}-{x}^{2}-2{x}+2$
171.1-j1
171.1-j
$1$
$1$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
171.1
\( 3^{2} \cdot 19 \)
\( 3^{4} \cdot 19^{2} \)
$2.81705$
$(-a-4), (-a+4), (a)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$1$
\( 2^{3} \)
$1.194156810$
$3.679988085$
8.065308033
\( -\frac{1404928}{171} \)
\( \bigl[0\) , \( 1\) , \( a\) , \( -2\) , \( -7\bigr] \)
${y}^2+a{y}={x}^{3}+{x}^{2}-2{x}-7$
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.