Atkin-Lehner |
2- 3+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
8784j |
Isogeny class |
Conductor |
8784 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2688 |
Modular degree for the optimal curve |
Δ |
-13492224 = -1 · 213 · 33 · 61 |
Discriminant |
Eigenvalues |
2- 3+ -1 -4 -6 -6 3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-123,554] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:24:1] [5:8:1] |
Generators of the group modulo torsion |
j |
-1860867/122 |
j-invariant |
L |
5.0289188020456 |
L(r)(E,1)/r! |
Ω |
2.2001378937355 |
Real period |
R |
0.28571611445168 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999995 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1098g1 35136bn1 8784i1 |
Quadratic twists by: -4 8 -3 |