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-a1 56.1-a $6$
$18$
\(\Q(\zeta_{7})^+\) $3$
$[3, 0]$
56.1
\( 2^{3} \cdot 7 \)
\( 2^{27} \cdot 7^{6} \)
$1.22349$
$(-a^2-a+2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
✓
$2, 3$
2B , 3B.1.2 $9$
\( 2 \cdot 3 \)
$1$
$0.288080952$
0.555584693
\( \frac{2251439055699625}{25088} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$
392.1-a1 392.1-a $6$
$18$
\(\Q(\zeta_{7})^+\) $3$
$[3, 0]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( 2^{27} \cdot 7^{12} \)
$1.69220$
$(-a^2-a+2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2B , 3B $1$
\( 2^{2} \)
$1$
$7.041603260$
1.005943322
\( \frac{2251439055699625}{25088} \)
\( \bigl[a^{2} - 2\) , \( -1\) , \( a^{2} + a - 2\) , \( -10922 a^{2} + 13652 a - 5462\) , \( 772040 a^{2} - 1158061 a + 386020\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}-{x}^{2}+\left(-10922a^{2}+13652a-5462\right){x}+772040a^{2}-1158061a+386020$
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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.
