Atkin-Lehner |
2- 3- 5- 7- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
48510dx |
Isogeny class |
Conductor |
48510 |
Conductor |
∏ cp |
1008 |
Product of Tamagawa factors cp |
deg |
1032192 |
Modular degree for the optimal curve |
Δ |
56330588160000000 = 218 · 36 · 57 · 73 · 11 |
Discriminant |
Eigenvalues |
2- 3- 5- 7- 11+ -2 8 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-1138682,467828281] |
[a1,a2,a3,a4,a6] |
Generators |
[241:-14521:1] |
Generators of the group modulo torsion |
j |
652993822364173263/225280000000 |
j-invariant |
L |
10.325363936319 |
L(r)(E,1)/r! |
Ω |
0.34611129531735 |
Real period |
R |
0.11838292181825 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999999 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
5390g1 48510cu1 |
Quadratic twists by: -3 -7 |