Atkin-Lehner |
2+ 3+ 7+ 13+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
109746b |
Isogeny class |
Conductor |
109746 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
69120 |
Modular degree for the optimal curve |
Δ |
-4719955968 = -1 · 212 · 33 · 72 · 13 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7+ -3 13+ 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-687,7853] |
[a1,a2,a3,a4,a6] |
Generators |
[-29:67:1] [-2:97:1] |
Generators of the group modulo torsion |
j |
-1329185824875/174813184 |
j-invariant |
L |
8.4829154738964 |
L(r)(E,1)/r! |
Ω |
1.3298945470525 |
Real period |
R |
0.79732971074522 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999973029 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
109746m1 |
Quadratic twists by: -3 |