Atkin-Lehner |
2+ 3- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
120384bn |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
103680 |
Modular degree for the optimal curve |
Δ |
-22417788096 = -1 · 26 · 36 · 113 · 192 |
Discriminant |
Eigenvalues |
2+ 3- -3 -4 11- -2 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-984,-13894] |
[a1,a2,a3,a4,a6] |
Generators |
[47:209:1] |
Generators of the group modulo torsion |
j |
-2258403328/480491 |
j-invariant |
L |
2.8192069730998 |
L(r)(E,1)/r! |
Ω |
0.42140638772917 |
Real period |
R |
1.1149993364945 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999704968 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
120384dc1 1881b1 13376c1 |
Quadratic twists by: -4 8 -3 |