Atkin-Lehner |
3+ 5+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
8325h |
Isogeny class |
Conductor |
8325 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
3456 |
Modular degree for the optimal curve |
Δ |
-78046875 = -1 · 33 · 57 · 37 |
Discriminant |
Eigenvalues |
-2 3+ 5+ -4 0 -1 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,75,-344] |
[a1,a2,a3,a4,a6] |
Generators |
[4:4:1] [10:37:1] |
Generators of the group modulo torsion |
j |
110592/185 |
j-invariant |
L |
2.9284228994188 |
L(r)(E,1)/r! |
Ω |
1.016282560758 |
Real period |
R |
0.36018807816065 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999993 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8325f1 1665b1 |
Quadratic twists by: -3 5 |