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
56.1-a3
56.1-a
$6$
$18$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
56.1
\( 2^{3} \cdot 7 \)
\( 2^{9} \cdot 7^{18} \)
$1.22349$
$(-a^2-a+2), (2)$
0
$\Z/6\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
✓
$2, 3$
2B , 3Cs.1.1
$1$
\( 2 \cdot 3^{2} \)
$1$
$7.778185713$
0.555584693
\( \frac{4956477625}{941192} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \)
${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$
392.1-a3
392.1-a
$6$
$18$
\(\Q(\zeta_{7})^+\)
$3$
$[3, 0]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{9} \cdot 7^{24} \)
$1.69220$
$(-a^2-a+2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
✓
$2, 3$
2B , 3Cs
$1$
\( 2^{2} \)
$1$
$7.041603260$
1.005943322
\( \frac{4956477625}{941192} \)
\( \bigl[a^{2} - 2\) , \( -1\) , \( a^{2} + a - 2\) , \( -142 a^{2} + 177 a - 72\) , \( 976 a^{2} - 1465 a + 488\bigr] \)
${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}-{x}^{2}+\left(-142a^{2}+177a-72\right){x}+976a^{2}-1465a+488$
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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.