Atkin-Lehner |
2+ 3- 5- 17- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
47430q |
Isogeny class |
Conductor |
47430 |
Conductor |
∏ cp |
120 |
Product of Tamagawa factors cp |
deg |
384000 |
Modular degree for the optimal curve |
Δ |
-21584015632800000 = -1 · 28 · 311 · 55 · 173 · 31 |
Discriminant |
Eigenvalues |
2+ 3- 5- -2 -3 1 17- -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-48969,8219533] |
[a1,a2,a3,a4,a6] |
Generators |
[-163:3524:1] [194:2351:1] |
Generators of the group modulo torsion |
j |
-17814140715089809/29607703200000 |
j-invariant |
L |
7.1952367095218 |
L(r)(E,1)/r! |
Ω |
0.34240245059066 |
Real period |
R |
0.17511646254063 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15810l1 |
Quadratic twists by: -3 |