Atkin-Lehner |
2+ 3- 23- |
Signs for the Atkin-Lehner involutions |
Class |
101568bc |
Isogeny class |
Conductor |
101568 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
36864 |
Modular degree for the optimal curve |
Δ |
336393216 = 210 · 33 · 233 |
Discriminant |
Eigenvalues |
2+ 3- 2 -2 0 -2 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-797,8355] |
[a1,a2,a3,a4,a6] |
Generators |
[31:120:1] |
Generators of the group modulo torsion |
j |
4499456/27 |
j-invariant |
L |
9.7630069236303 |
L(r)(E,1)/r! |
Ω |
1.7192552905825 |
Real period |
R |
1.8928751635134 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000005922 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
101568cj1 12696n1 101568bk1 |
Quadratic twists by: -4 8 -23 |