Atkin-Lehner |
2- 3- 5+ 7+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
76860d |
Isogeny class |
Conductor |
76860 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
93312 |
Modular degree for the optimal curve |
Δ |
-1245132000000 = -1 · 28 · 36 · 56 · 7 · 61 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7+ -4 0 -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-768,54308] |
[a1,a2,a3,a4,a6] |
Generators |
[-44:54:1] [-16:250:1] |
Generators of the group modulo torsion |
j |
-268435456/6671875 |
j-invariant |
L |
9.6693366738066 |
L(r)(E,1)/r! |
Ω |
0.72248709243276 |
Real period |
R |
1.1152836702395 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000019 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8540f1 |
Quadratic twists by: -3 |