Atkin-Lehner |
3+ 5- 31- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
115785c |
Isogeny class |
Conductor |
115785 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
-651539678535 = -1 · 39 · 5 · 312 · 832 |
Discriminant |
Eigenvalues |
1 3+ 5- -4 -2 4 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,1956,-20485] |
[a1,a2,a3,a4,a6] |
Generators |
[12558:265529:27] |
Generators of the group modulo torsion |
j |
42035292333/33101645 |
j-invariant |
L |
6.7502707457223 |
L(r)(E,1)/r! |
Ω |
0.50623110106543 |
Real period |
R |
6.6671829678341 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999942218 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
115785a1 |
Quadratic twists by: -3 |