Atkin-Lehner |
2+ 3- 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
76608bw |
Isogeny class |
Conductor |
76608 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
192683970920448 = 218 · 37 · 72 · 193 |
Discriminant |
Eigenvalues |
2+ 3- 4 7+ -2 -4 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-248268,-47608720] |
[a1,a2,a3,a4,a6] |
Generators |
[1285:41895:1] |
Generators of the group modulo torsion |
j |
8855610342769/1008273 |
j-invariant |
L |
8.536426244285 |
L(r)(E,1)/r! |
Ω |
0.21388106370207 |
Real period |
R |
3.326002038757 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999967079 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
76608fd1 1197c1 25536l1 |
Quadratic twists by: -4 8 -3 |