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
72.1-a4
72.1-a
$6$
$8$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{8} \)
$2.26923$
$(-3a+13), (-a-4), (-a+4)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$9.301119475$
0.533455787
\( \frac{1556068}{81} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 80669 a - 351598\) , \( 24796372 a - 108084830\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(80669a-351598\right){x}+24796372a-108084830$
72.1-j4
72.1-j
$6$
$8$
\(\Q(\sqrt{19}) \)
$2$
$[2, 0]$
72.1
\( 2^{3} \cdot 3^{2} \)
\( 2^{8} \cdot 3^{8} \)
$2.26923$
$(-3a+13), (-a-4), (-a+4)$
$1$
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2Cs
$1$
\( 2^{6} \)
$0.781297541$
$22.73403407$
4.074892574
\( \frac{1556068}{81} \)
\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 80668 a - 351601\) , \( -24905977 a + 108562673\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(80668a-351601\right){x}-24905977a+108562673$
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.