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
$6$
$8$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
126.1
\( 2 \cdot 3^{2} \cdot 7 \)
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \)
$2.24040$
$(-a+4), (-2a+7), (3)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{7} \)
$1.141519658$
$2.486887276$
6.069675380
\( \frac{65597103937}{63504} \)
\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -10083 a - 37721\) , \( -1075140 a - 4022809\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10083a-37721\right){x}-1075140a-4022809$
126.1-b5
126.1-b
$6$
$8$
\(\Q(\sqrt{14}) \)
$2$
$[2, 0]$
126.1
\( 2 \cdot 3^{2} \cdot 7 \)
\( 2^{8} \cdot 3^{8} \cdot 7^{4} \)
$2.24040$
$(-a+4), (-2a+7), (3)$
0
$\Z/2\Z\oplus\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{6} \)
$1$
$12.07873502$
1.614088862
\( \frac{65597103937}{63504} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-84{x}+261$
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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.