Atkin-Lehner |
3- 5+ 7+ 13+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69615f |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
27648 |
Modular degree for the optimal curve |
Δ |
-862738695 = -1 · 38 · 5 · 7 · 13 · 172 |
Discriminant |
Eigenvalues |
-1 3- 5+ 7+ -2 13+ 17+ -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-68,1446] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:26:1] [-4:42:1] |
Generators of the group modulo torsion |
j |
-47045881/1183455 |
j-invariant |
L |
5.9736353310441 |
L(r)(E,1)/r! |
Ω |
1.3244002431371 |
Real period |
R |
2.2552228308358 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000116 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23205e1 |
Quadratic twists by: -3 |