Atkin-Lehner |
3- 7+ 17+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
77469q |
Isogeny class |
Conductor |
77469 |
Conductor |
∏ cp |
35 |
Product of Tamagawa factors cp |
deg |
856800 |
Modular degree for the optimal curve |
Δ |
-738577675534367781 = -1 · 37 · 74 · 173 · 315 |
Discriminant |
Eigenvalues |
1 3- -2 7+ 1 -4 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,193083,-25346135] |
[a1,a2,a3,a4,a6] |
Generators |
[155:2805:1] |
Generators of the group modulo torsion |
j |
331563640418853143/307612526253381 |
j-invariant |
L |
6.3984999768042 |
L(r)(E,1)/r! |
Ω |
0.15590271389362 |
Real period |
R |
1.1726177209491 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999997722 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
77469j1 |
Quadratic twists by: -7 |