Atkin-Lehner |
2- 7+ 11+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
50666j |
Isogeny class |
Conductor |
50666 |
Conductor |
∏ cp |
138 |
Product of Tamagawa factors cp |
deg |
313536 |
Modular degree for the optimal curve |
Δ |
489407320686592 = 223 · 74 · 11 · 472 |
Discriminant |
Eigenvalues |
2- -1 -4 7+ 11+ -5 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-24550,-1039389] |
[a1,a2,a3,a4,a6] |
Generators |
[-127:287:1] [-99:707:1] |
Generators of the group modulo torsion |
j |
681533404492801/203834785792 |
j-invariant |
L |
9.027922370233 |
L(r)(E,1)/r! |
Ω |
0.39021623235189 |
Real period |
R |
0.16764993841037 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
50666m1 |
Quadratic twists by: -7 |