Atkin-Lehner |
2+ 3- 11- 43+ |
Signs for the Atkin-Lehner involutions |
Class |
68112l |
Isogeny class |
Conductor |
68112 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
71680 |
Modular degree for the optimal curve |
Δ |
726979060368 = 24 · 38 · 115 · 43 |
Discriminant |
Eigenvalues |
2+ 3- 0 -1 11- 4 2 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3675,75301] |
[a1,a2,a3,a4,a6] |
Generators |
[20:99:1] |
Generators of the group modulo torsion |
j |
470596000000/62326737 |
j-invariant |
L |
7.2413390819375 |
L(r)(E,1)/r! |
Ω |
0.86840137098784 |
Real period |
R |
0.83387006558254 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000223 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34056v1 22704i1 |
Quadratic twists by: -4 -3 |