Atkin-Lehner |
2- 3+ 7+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
63168bw |
Isogeny class |
Conductor |
63168 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
98304 |
Modular degree for the optimal curve |
Δ |
-1064957902848 = -1 · 220 · 32 · 74 · 47 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ 2 0 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-6209,196833] |
[a1,a2,a3,a4,a6] |
Generators |
[-37:612:1] [7:392:1] |
Generators of the group modulo torsion |
j |
-100999381393/4062492 |
j-invariant |
L |
8.0547009456667 |
L(r)(E,1)/r! |
Ω |
0.86678868904515 |
Real period |
R |
2.3231443394044 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000008 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
63168br1 15792ba1 |
Quadratic twists by: -4 8 |