Atkin-Lehner |
5+ 7- 37- |
Signs for the Atkin-Lehner involutions |
Class |
45325k |
Isogeny class |
Conductor |
45325 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
269568 |
Modular degree for the optimal curve |
Δ |
42509892578125 = 510 · 76 · 37 |
Discriminant |
Eigenvalues |
2 1 5+ 7- 3 -2 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-191508,-32319731] |
[a1,a2,a3,a4,a6] |
Generators |
[-593895025358449094822:-56348884791470904813:2358085875457285576] |
Generators of the group modulo torsion |
j |
422550360064/23125 |
j-invariant |
L |
13.889232291466 |
L(r)(E,1)/r! |
Ω |
0.22822018948537 |
Real period |
R |
30.429455699747 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9065e1 925d1 |
Quadratic twists by: 5 -7 |