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
392.1-c1
392.1-c
$4$
$4$
\(\Q(\sqrt{11}) \)
$2$
$[2, 0]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{4} \cdot 7^{2} \)
$2.63746$
$(a+3), (a+2), (a-2)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2 \)
$1$
$24.47471212$
1.844850840
\( \frac{432}{7} \)
\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 18 a + 61\) , \( 342 a + 1134\bigr] \)
${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(18a+61\right){x}+342a+1134$
392.1-f1
392.1-f
$4$
$4$
\(\Q(\sqrt{11}) \)
$2$
$[2, 0]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{4} \cdot 7^{2} \)
$2.63746$
$(a+3), (a+2), (a-2)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2 \)
$3.287005482$
$10.54517411$
5.225499916
\( \frac{432}{7} \)
\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 17 a + 55\) , \( -257 a - 854\bigr] \)
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(17a+55\right){x}-257a-854$
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.