Atkin-Lehner |
2- 7- 89- |
Signs for the Atkin-Lehner involutions |
Class |
69776z |
Isogeny class |
Conductor |
69776 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
-42888237056 = -1 · 212 · 76 · 89 |
Discriminant |
Eigenvalues |
2- -1 1 7- 2 -2 -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-800,13504] |
[a1,a2,a3,a4,a6] |
Generators |
[-30:98:1] [26:98:1] |
Generators of the group modulo torsion |
j |
-117649/89 |
j-invariant |
L |
9.2613584370662 |
L(r)(E,1)/r! |
Ω |
1.0493477866487 |
Real period |
R |
1.1032279472735 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999387 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4361c1 1424b1 |
Quadratic twists by: -4 -7 |