Atkin-Lehner |
3- 11- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
72963m |
Isogeny class |
Conductor |
72963 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
39168 |
Modular degree for the optimal curve |
Δ |
-3563731809 = -1 · 38 · 112 · 672 |
Discriminant |
Eigenvalues |
-1 3- 3 0 11- -3 -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-716,8088] |
[a1,a2,a3,a4,a6] |
Generators |
[12:-40:1] |
Generators of the group modulo torsion |
j |
-459601153/40401 |
j-invariant |
L |
4.6594900113017 |
L(r)(E,1)/r! |
Ω |
1.3742096152277 |
Real period |
R |
0.84766726245577 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002103 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24321d1 72963k1 |
Quadratic twists by: -3 -11 |