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
126.1-a5
126.1-a
$8$
$16$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
126.1
\( 2 \cdot 3^{2} \cdot 7 \)
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \)
$1.58420$
$(a+3), (-a+2), (-a-2), (a)$
0
$\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{9} \)
$1$
$2.486887276$
3.759820155
\( \frac{84448510979617}{933897762} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( -913\) , \( 10001\bigr] \)
${y}^2+a{x}{y}={x}^{3}-913{x}+10001$
126.1-f5
126.1-f
$8$
$16$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
126.1
\( 2 \cdot 3^{2} \cdot 7 \)
\( 2^{2} \cdot 3^{8} \cdot 7^{16} \)
$1.58420$
$(a+3), (-a+2), (-a-2), (a)$
$1$
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2B
$1$
\( 2^{4} \)
$2.310811814$
$0.754920939$
2.637406196
\( \frac{84448510979617}{933897762} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-914{x}-10915$
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.