Atkin-Lehner |
2+ 3+ 19+ 79- |
Signs for the Atkin-Lehner involutions |
Class |
72048b |
Isogeny class |
Conductor |
72048 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
10880 |
Modular degree for the optimal curve |
Δ |
-5835888 = -1 · 24 · 35 · 19 · 79 |
Discriminant |
Eigenvalues |
2+ 3+ -2 2 0 -4 -7 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-24,-117] |
[a1,a2,a3,a4,a6] |
Generators |
[7:3:1] [143:1703:1] |
Generators of the group modulo torsion |
j |
-99588352/364743 |
j-invariant |
L |
8.3306099440451 |
L(r)(E,1)/r! |
Ω |
0.98474500841059 |
Real period |
R |
8.459662016923 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000048 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
36024e1 |
Quadratic twists by: -4 |