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
8192.6-a1
8192.6-a
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
8192.6
\( 2^{13} \)
\( 2^{21} \)
$2.24924$
$(a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2^{2} \)
$0.581060258$
$4.088009945$
3.591237173
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -a - 2\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(-a-2\right){x}$
8192.6-a2
8192.6-a
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
8192.6
\( 2^{13} \)
\( 2^{21} \)
$2.24924$
$(a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2^{3} \)
$0.290530129$
$4.088009945$
3.591237173
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a - 2\) , \( 0\bigr] \)
${y}^2={x}^{3}+\left(2a-2\right){x}$
8192.6-b1
8192.6-b
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
8192.6
\( 2^{13} \)
\( 2^{15} \)
$2.24924$
$(a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2^{2} \)
$0.414505375$
$5.781319108$
3.622997884
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( a\) , \( 0\bigr] \)
${y}^2={x}^{3}+a{x}$
8192.6-b2
8192.6-b
$2$
$2$
\(\Q(\sqrt{-7}) \)
$2$
$[0, 1]$
8192.6
\( 2^{13} \)
\( 2^{27} \)
$2.24924$
$(a), (-a+1)$
$1$
$\Z/2\Z$
$\textsf{potential}$
$-4$
$N(\mathrm{U}(1))$
✓
✓
$1$
\( 2^{2} \)
$0.829010751$
$2.890659554$
3.622997884
\( 1728 \)
\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a\) , \( 0\bigr] \)
${y}^2={x}^{3}-4a{x}$
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.