Atkin-Lehner |
2- 3+ 5- 17- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
42330z |
Isogeny class |
Conductor |
42330 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
406368000 = 28 · 32 · 53 · 17 · 83 |
Discriminant |
Eigenvalues |
2- 3+ 5- -4 -5 -3 17- -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-255,1125] |
[a1,a2,a3,a4,a6] |
Generators |
[-17:38:1] [3:18:1] |
Generators of the group modulo torsion |
j |
1834216913521/406368000 |
j-invariant |
L |
10.677480907488 |
L(r)(E,1)/r! |
Ω |
1.587701975065 |
Real period |
R |
0.14010659582186 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
126990s1 |
Quadratic twists by: -3 |