Atkin-Lehner |
2+ 5+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
75200w |
Isogeny class |
Conductor |
75200 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
359424 |
Modular degree for the optimal curve |
Δ |
-118594784460800 = -1 · 231 · 52 · 472 |
Discriminant |
Eigenvalues |
2+ -1 5+ -4 -5 4 -5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-49153,4243457] |
[a1,a2,a3,a4,a6] |
Generators |
[-104:2867:1] [1:2048:1] |
Generators of the group modulo torsion |
j |
-2004023020585/18096128 |
j-invariant |
L |
7.2175240940791 |
L(r)(E,1)/r! |
Ω |
0.59274137010739 |
Real period |
R |
1.5220643559859 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000013 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
75200cf1 2350k1 75200bg1 |
Quadratic twists by: -4 8 5 |