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-a6 56.1-a $6$
$18$
\(\Q(\zeta_{7})^+\) $3$
$[3, 0]$
56.1
\( 2^{3} \cdot 7 \)
\( - 2^{18} \cdot 7^{9} \)
$1.22349$
$(-a^2-a+2), (2)$
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
\( \frac{9938375}{21952} \)
\( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$
392.1-a6 392.1-a $6$
$18$
\(\Q(\zeta_{7})^+\) $3$
$[3, 0]$
392.1
\( 2^{3} \cdot 7^{2} \)
\( - 2^{18} \cdot 7^{15} \)
$1.69220$
$(-a^2-a+2), (2)$
0
$\Z/2\Z$
$\textsf{no}$
$\mathrm{SU}(2)$ ✓
✓
$2, 3$
2B , 3Cs $1$
\( 2^{2} \)
$1$
$7.041603260$
1.005943322
\( \frac{9938375}{21952} \)
\( \bigl[a^{2} - 2\) , \( -1\) , \( a^{2} + a - 2\) , \( 18 a^{2} - 23 a + 8\) , \( 80 a^{2} - 121 a + 40\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}-{x}^{2}+\left(18a^{2}-23a+8\right){x}+80a^{2}-121a+40$
Download
displayed columns for
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*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.
