Atkin-Lehner |
3+ 5- 11- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
76725i |
Isogeny class |
Conductor |
76725 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
42240 |
Modular degree for the optimal curve |
Δ |
-838987875 = -1 · 39 · 53 · 11 · 31 |
Discriminant |
Eigenvalues |
2 3+ 5- -1 11- -2 6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-135,-1519] |
[a1,a2,a3,a4,a6] |
Generators |
[1764:7987:64] |
Generators of the group modulo torsion |
j |
-110592/341 |
j-invariant |
L |
12.172100309891 |
L(r)(E,1)/r! |
Ω |
0.64657160217745 |
Real period |
R |
4.7064007553301 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
76725e1 76725j1 |
Quadratic twists by: -3 5 |