Atkin-Lehner |
2+ 7- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
69776b |
Isogeny class |
Conductor |
69776 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
-525380903936 = -1 · 210 · 78 · 89 |
Discriminant |
Eigenvalues |
2+ -1 -3 7- -2 0 3 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-10992,448624] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:686:1] [54:-98:1] |
Generators of the group modulo torsion |
j |
-1219284868/4361 |
j-invariant |
L |
7.0548342657959 |
L(r)(E,1)/r! |
Ω |
0.93063820287117 |
Real period |
R |
0.94758014499713 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000009 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34888d1 9968b1 |
Quadratic twists by: -4 -7 |