Atkin-Lehner |
2+ 3- 7- 47- |
Signs for the Atkin-Lehner involutions |
Class |
63168bs |
Isogeny class |
Conductor |
63168 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
225280 |
Modular degree for the optimal curve |
Δ |
67419947234304 = 210 · 35 · 78 · 47 |
Discriminant |
Eigenvalues |
2+ 3- -2 7- -4 2 -6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-18429,-884349] |
[a1,a2,a3,a4,a6] |
Generators |
[-90:231:1] [-69:252:1] |
Generators of the group modulo torsion |
j |
676009238591488/65839792221 |
j-invariant |
L |
10.853863303285 |
L(r)(E,1)/r! |
Ω |
0.41231848756485 |
Real period |
R |
1.3161989615592 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999945 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
63168bx1 7896j1 |
Quadratic twists by: -4 8 |