Atkin-Lehner |
2+ 3- 19+ 79- |
Signs for the Atkin-Lehner involutions |
Class |
72048h |
Isogeny class |
Conductor |
72048 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
30080 |
Modular degree for the optimal curve |
Δ |
1418120784 = 24 · 310 · 19 · 79 |
Discriminant |
Eigenvalues |
2+ 3- -2 -4 0 2 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-419,-2904] |
[a1,a2,a3,a4,a6] |
Generators |
[28:90:1] |
Generators of the group modulo torsion |
j |
509661571072/88632549 |
j-invariant |
L |
5.1356386252057 |
L(r)(E,1)/r! |
Ω |
1.0675627245388 |
Real period |
R |
1.9242480114365 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001483 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
36024a1 |
Quadratic twists by: -4 |