Atkin-Lehner |
2+ 5- 29+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
68150i |
Isogeny class |
Conductor |
68150 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
69984 |
Modular degree for the optimal curve |
Δ |
120434680000 = 26 · 54 · 29 · 473 |
Discriminant |
Eigenvalues |
2+ 1 5- 2 0 -4 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-5201,142948] |
[a1,a2,a3,a4,a6] |
Generators |
[-53:546:1] |
Generators of the group modulo torsion |
j |
24887668665625/192695488 |
j-invariant |
L |
5.3382756835592 |
L(r)(E,1)/r! |
Ω |
1.0529995518545 |
Real period |
R |
2.5347948506328 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000076 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
68150m1 |
Quadratic twists by: 5 |