Atkin-Lehner |
2+ 5+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
48400b |
Isogeny class |
Conductor |
48400 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
193536 |
Modular degree for the optimal curve |
Δ |
-3327500000000000 = -1 · 211 · 513 · 113 |
Discriminant |
Eigenvalues |
2+ 1 5+ -3 11+ -4 3 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,5592,-2768812] |
[a1,a2,a3,a4,a6] |
Generators |
[538:12500:1] |
Generators of the group modulo torsion |
j |
453962/78125 |
j-invariant |
L |
5.4426626101407 |
L(r)(E,1)/r! |
Ω |
0.21082586210196 |
Real period |
R |
0.80674735475887 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000081 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
24200a1 9680a1 48400a1 |
Quadratic twists by: -4 5 -11 |