Atkin-Lehner |
2- 3- 7+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
68544ec |
Isogeny class |
Conductor |
68544 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
71680 |
Modular degree for the optimal curve |
Δ |
-84996547776 = -1 · 26 · 313 · 72 · 17 |
Discriminant |
Eigenvalues |
2- 3- -3 7+ 3 -1 17- -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1524,26854] |
[a1,a2,a3,a4,a6] |
Generators |
[47:-243:1] [23:63:1] |
Generators of the group modulo torsion |
j |
-8390176768/1821771 |
j-invariant |
L |
8.8606814248986 |
L(r)(E,1)/r! |
Ω |
1.0312100659827 |
Real period |
R |
1.0740635828182 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000043 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68544cq1 17136bg1 22848cm1 |
Quadratic twists by: -4 8 -3 |