Atkin-Lehner |
2+ 3- 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
76608ba |
Isogeny class |
Conductor |
76608 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
688128 |
Modular degree for the optimal curve |
Δ |
354204320231559168 = 212 · 37 · 78 · 193 |
Discriminant |
Eigenvalues |
2+ 3- 0 7+ 4 -4 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-189300,13602976] |
[a1,a2,a3,a4,a6] |
j |
251239591000000/118622310177 |
j-invariant |
L |
2.1620580026353 |
L(r)(E,1)/r! |
Ω |
0.2702572531628 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
76608cm1 38304bk1 25536y1 |
Quadratic twists by: -4 8 -3 |