Atkin-Lehner |
3- 5+ 7- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
50715t |
Isogeny class |
Conductor |
50715 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
838656 |
Modular degree for the optimal curve |
Δ |
-332942338525590675 = -1 · 315 · 52 · 79 · 23 |
Discriminant |
Eigenvalues |
2 3- 5+ 7- 3 2 -4 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-99813,30298819] |
[a1,a2,a3,a4,a6] |
Generators |
[242:41801:8] |
Generators of the group modulo torsion |
j |
-3738308608/11317725 |
j-invariant |
L |
12.105028924166 |
L(r)(E,1)/r! |
Ω |
0.26764451997178 |
Real period |
R |
5.6535012025609 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16905r1 50715bp1 |
Quadratic twists by: -3 -7 |