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
8712.5-c4
8712.5-c
$4$
$4$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
8712.5
\( 2^{3} \cdot 3^{2} \cdot 11^{2} \)
\( 2^{10} \cdot 3^{8} \cdot 11^{2} \)
$2.44182$
$(a), (-a-1), (a-1), (a+3), (a-3)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{3} \)
$0.823221395$
$1.307767102$
3.045033333
\( \frac{5690357426}{891} \)
\( \bigl[a\) , \( 1\) , \( a\) , \( -117\) , \( -513\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-117{x}-513$
17424.5-l4
17424.5-l
$4$
$4$
\(\Q(\sqrt{-2}) \)
$2$
$[0, 1]$
17424.5
\( 2^{4} \cdot 3^{2} \cdot 11^{2} \)
\( 2^{10} \cdot 3^{8} \cdot 11^{2} \)
$2.90383$
$(a), (-a-1), (a-1), (a+3), (a-3)$
0
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$1$
\( 2^{6} \)
$1$
$1.307767102$
3.698923945
\( \frac{5690357426}{891} \)
\( \bigl[a\) , \( 0\) , \( a\) , \( -117\) , \( 514\bigr] \)
${y}^2+a{x}{y}+a{y}={x}^{3}-117{x}+514$
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*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.