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-a8
126.1-a
$8$
$16$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
126.1
\( 2 \cdot 3^{2} \cdot 7 \)
\( - 2^{2} \cdot 3^{2} \cdot 7 \)
$1.58420$
$(a+3), (-a+2), (-a-2), (a)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$256$
\( 2 \)
$1$
$0.155430454$
3.759820155
\( \frac{9010577383592310868608127}{42} a + 567613022049721543828200 \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( -3810 a - 11423\) , \( -228018 a - 623037\bigr] \)
${y}^2+a{x}{y}={x}^{3}+\left(-3810a-11423\right){x}-228018a-623037$
126.1-f8
126.1-f
$8$
$16$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
126.1
\( 2 \cdot 3^{2} \cdot 7 \)
\( - 2^{2} \cdot 3^{2} \cdot 7 \)
$1.58420$
$(a+3), (-a+2), (-a-2), (a)$
$1$
$\Z/4\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2$
2B
$4$
\( 2 \)
$2.310811814$
$6.039367514$
2.637406196
\( \frac{9010577383592310868608127}{42} a + 567613022049721543828200 \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -3810 a - 11424\) , \( 224208 a + 611613\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-3810a-11424\right){x}+224208a+611613$
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Pari/GP
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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.