Atkin-Lehner |
2- 3- 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
76608eo |
Isogeny class |
Conductor |
76608 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
300234719232 = 214 · 39 · 72 · 19 |
Discriminant |
Eigenvalues |
2- 3- -4 7+ -2 4 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-6492,199600] |
[a1,a2,a3,a4,a6] |
Generators |
[56:-108:1] [-22:576:1] |
Generators of the group modulo torsion |
j |
2533446736/25137 |
j-invariant |
L |
8.1912412265678 |
L(r)(E,1)/r! |
Ω |
0.97518243295808 |
Real period |
R |
1.0499626723504 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998356 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
76608ck1 19152o1 25536cz1 |
Quadratic twists by: -4 8 -3 |