Atkin-Lehner |
2+ 3+ 5+ 11+ 103+ |
Signs for the Atkin-Lehner involutions |
Class |
33990b |
Isogeny class |
Conductor |
33990 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
8448 |
Modular degree for the optimal curve |
Δ |
-2991120 = -1 · 24 · 3 · 5 · 112 · 103 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -1 11+ 2 3 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-88,-368] |
[a1,a2,a3,a4,a6] |
Generators |
[12:16:1] |
Generators of the group modulo torsion |
j |
-76711450249/2991120 |
j-invariant |
L |
3.0810168311635 |
L(r)(E,1)/r! |
Ω |
0.77645507982977 |
Real period |
R |
0.99201386892823 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999998 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
101970cj1 |
Quadratic twists by: -3 |