Atkin-Lehner |
3+ 11+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
8217b |
Isogeny class |
Conductor |
8217 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
10944 |
Modular degree for the optimal curve |
Δ |
1491558057 = 39 · 11 · 832 |
Discriminant |
Eigenvalues |
-1 3+ 0 2 11+ -2 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-42635,-3377726] |
[a1,a2,a3,a4,a6] |
j |
435433333084875/75779 |
j-invariant |
L |
1.3289810229462 |
L(r)(E,1)/r! |
Ω |
0.33224525573656 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8217c1 90387a1 |
Quadratic twists by: -3 -11 |