Atkin-Lehner |
2- 3+ 23- 59- |
Signs for the Atkin-Lehner involutions |
Class |
65136q |
Isogeny class |
Conductor |
65136 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-82840485888 = -1 · 215 · 34 · 232 · 59 |
Discriminant |
Eigenvalues |
2- 3+ -2 -3 1 -5 5 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1344,-23040] |
[a1,a2,a3,a4,a6] |
Generators |
[48:144:1] [66:-414:1] |
Generators of the group modulo torsion |
j |
-65597103937/20224728 |
j-invariant |
L |
7.2483537082541 |
L(r)(E,1)/r! |
Ω |
0.38809060045337 |
Real period |
R |
1.1673101750841 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000048 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8142h1 |
Quadratic twists by: -4 |