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
3844.2-a1
3844.2-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3844.2
\( 2^{2} \cdot 31^{2} \)
\( 2^{8} \cdot 31^{2} \)
$1.21869$
$(-6a+1), (6a-5), (2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$4.965180901$
1.433324264
\( -\frac{35937}{496} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 1\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}+1$
3844.2-a2
3844.2-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3844.2
\( 2^{2} \cdot 31^{2} \)
\( 2^{2} \cdot 31^{8} \)
$1.21869$
$(-6a+1), (6a-5), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{2} \)
$1$
$1.241295225$
1.433324264
\( \frac{3196010817}{1847042} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -31\) , \( 5\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-31{x}+5$
3844.2-a3
3844.2-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3844.2
\( 2^{2} \cdot 31^{2} \)
\( 2^{4} \cdot 31^{4} \)
$1.21869$
$(-6a+1), (6a-5), (2)$
0
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{3} \)
$1$
$2.482590450$
1.433324264
\( \frac{979146657}{3844} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -21\) , \( 41\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-21{x}+41$
3844.2-a4
3844.2-a
$4$
$4$
\(\Q(\sqrt{-3}) \)
$2$
$[0, 1]$
3844.2
\( 2^{2} \cdot 31^{2} \)
\( 2^{2} \cdot 31^{2} \)
$1.21869$
$(-6a+1), (6a-5), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$4$
\( 1 \)
$1$
$1.241295225$
1.433324264
\( \frac{3999236143617}{62} \)
\( \bigl[1\) , \( -1\) , \( 1\) , \( -331\) , \( 2397\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-331{x}+2397$
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.