Atkin-Lehner |
2+ 5+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
113600bc |
Isogeny class |
Conductor |
113600 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-264293580800 = -1 · 221 · 52 · 712 |
Discriminant |
Eigenvalues |
2+ -1 5+ -4 -1 -4 -7 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-3713,91777] |
[a1,a2,a3,a4,a6] |
Generators |
[33:-64:1] [3:284:1] |
Generators of the group modulo torsion |
j |
-864043465/40328 |
j-invariant |
L |
7.6309082176452 |
L(r)(E,1)/r! |
Ω |
0.97131572532742 |
Real period |
R |
0.98203241434547 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000003886 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
113600ca1 3550n1 113600br1 |
Quadratic twists by: -4 8 5 |