Atkin-Lehner |
2- 3+ 13- 83+ |
Signs for the Atkin-Lehner involutions |
Class |
51792i |
Isogeny class |
Conductor |
51792 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
59904 |
Modular degree for the optimal curve |
Δ |
-11031281664 = -1 · 218 · 3 · 132 · 83 |
Discriminant |
Eigenvalues |
2- 3+ 3 2 -5 13- 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1944,34032] |
[a1,a2,a3,a4,a6] |
Generators |
[34:78:1] |
Generators of the group modulo torsion |
j |
-198461344537/2693184 |
j-invariant |
L |
6.8452839537072 |
L(r)(E,1)/r! |
Ω |
1.2825601011419 |
Real period |
R |
1.3343008151453 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6474j1 |
Quadratic twists by: -4 |