Atkin-Lehner |
3+ 7- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
50127f |
Isogeny class |
Conductor |
50127 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
129024 |
Modular degree for the optimal curve |
Δ |
110346090915753 = 36 · 79 · 112 · 31 |
Discriminant |
Eigenvalues |
-1 3+ 2 7- 11+ -2 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-23717,1301978] |
[a1,a2,a3,a4,a6] |
Generators |
[-174:532:1] |
Generators of the group modulo torsion |
j |
36561310759/2734479 |
j-invariant |
L |
3.1633830383473 |
L(r)(E,1)/r! |
Ω |
0.5808726988527 |
Real period |
R |
2.7229572371044 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999977 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
50127m1 |
Quadratic twists by: -7 |