Atkin-Lehner |
2- 3+ 5- 7+ 11- 17- |
Signs for the Atkin-Lehner involutions |
Class |
39270cd |
Isogeny class |
Conductor |
39270 |
Conductor |
∏ cp |
768 |
Product of Tamagawa factors cp |
deg |
1032192 |
Modular degree for the optimal curve |
Δ |
-3970489523298144000 = -1 · 28 · 3 · 53 · 72 · 112 · 178 |
Discriminant |
Eigenvalues |
2- 3+ 5- 7+ 11- -2 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-399125,136253435] |
[a1,a2,a3,a4,a6] |
Generators |
[-727:6908:1] |
Generators of the group modulo torsion |
j |
-7031541993398949474001/3970489523298144000 |
j-invariant |
L |
7.8077226628882 |
L(r)(E,1)/r! |
Ω |
0.22975383205984 |
Real period |
R |
0.70797900236044 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999976 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
117810t1 |
Quadratic twists by: -3 |