Atkin-Lehner |
2- 3+ 11- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
50094bk |
Isogeny class |
Conductor |
50094 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
-6195984993792 = -1 · 29 · 33 · 117 · 23 |
Discriminant |
Eigenvalues |
2- 3+ 0 3 11- 1 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-90410,10486633] |
[a1,a2,a3,a4,a6] |
Generators |
[289:2759:1] |
Generators of the group modulo torsion |
j |
-1708632808875/129536 |
j-invariant |
L |
10.727188951363 |
L(r)(E,1)/r! |
Ω |
0.71841749183798 |
Real period |
R |
0.20738461566964 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000029 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
50094f1 4554d1 |
Quadratic twists by: -3 -11 |