Atkin-Lehner |
2+ 41+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
56416b |
Isogeny class |
Conductor |
56416 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
8192 |
Modular degree for the optimal curve |
Δ |
-7221248 = -1 · 212 · 41 · 43 |
Discriminant |
Eigenvalues |
2+ 0 -2 3 -2 -4 0 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-136,624] |
[a1,a2,a3,a4,a6] |
Generators |
[4:12:1] |
Generators of the group modulo torsion |
j |
-67917312/1763 |
j-invariant |
L |
4.7831174134073 |
L(r)(E,1)/r! |
Ω |
2.3500344108947 |
Real period |
R |
1.0176696543715 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000003 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
56416n1 112832g1 |
Quadratic twists by: -4 8 |