Atkin-Lehner |
2- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
75712cs |
Isogeny class |
Conductor |
75712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
129024 |
Modular degree for the optimal curve |
Δ |
-57572015341568 = -1 · 217 · 7 · 137 |
Discriminant |
Eigenvalues |
2- -1 0 7- -3 13+ 4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5633,401569] |
[a1,a2,a3,a4,a6] |
Generators |
[-69:676:1] |
Generators of the group modulo torsion |
j |
-31250/91 |
j-invariant |
L |
4.6450047322745 |
L(r)(E,1)/r! |
Ω |
0.55152407509889 |
Real period |
R |
1.0527656321905 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999990453 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
75712e1 18928d1 5824u1 |
Quadratic twists by: -4 8 13 |