Atkin-Lehner |
2+ 7+ 11+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
89474a |
Isogeny class |
Conductor |
89474 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
191808 |
Modular degree for the optimal curve |
Δ |
-85051459085824 = -1 · 29 · 74 · 112 · 833 |
Discriminant |
Eigenvalues |
2+ 0 -1 7+ 11+ -1 2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,5920,-409088] |
[a1,a2,a3,a4,a6] |
Generators |
[69:535:1] |
Generators of the group modulo torsion |
j |
9555543772551/35423348224 |
j-invariant |
L |
3.0057728613204 |
L(r)(E,1)/r! |
Ω |
0.30820686452324 |
Real period |
R |
4.8762263405441 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999969089 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89474c1 |
Quadratic twists by: -7 |