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-a4
126.1-a
$8$
$16$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
126.1
\( 2 \cdot 3^{2} \cdot 7 \)
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \)
$1.58420$
$(a+3), (-a+2), (-a-2), (a)$
0
$\Z/2\Z\oplus\Z/8\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{11} \)
$1$
$2.486887276$
3.759820155
\( \frac{124475734657}{63011844} \)
\( \bigl[a\) , \( 0\) , \( 0\) , \( -103\) , \( -205\bigr] \)
${y}^2+a{x}{y}={x}^{3}-103{x}-205$
126.1-f4
126.1-f
$8$
$16$
\(\Q(\sqrt{7}) \)
$2$
$[2, 0]$
126.1
\( 2 \cdot 3^{2} \cdot 7 \)
\( 2^{4} \cdot 3^{16} \cdot 7^{8} \)
$1.58420$
$(a+3), (-a+2), (-a-2), (a)$
$1$
$\Z/2\Z\oplus\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2$
2Cs
$1$
\( 2^{5} \)
$1.155405907$
$3.019683757$
2.637406196
\( \frac{124475734657}{63011844} \)
\( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-104{x}+101$
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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.