Atkin-Lehner |
2+ 3- 59- |
Signs for the Atkin-Lehner involutions |
Class |
33984y |
Isogeny class |
Conductor |
33984 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
175104 |
Modular degree for the optimal curve |
Δ |
-5911386827784192 = -1 · 237 · 36 · 59 |
Discriminant |
Eigenvalues |
2+ 3- 2 -3 1 -3 1 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,31956,2974768] |
[a1,a2,a3,a4,a6] |
Generators |
[269:5571:1] |
Generators of the group modulo torsion |
j |
18884848247/30932992 |
j-invariant |
L |
5.7236776648249 |
L(r)(E,1)/r! |
Ω |
0.2908255050604 |
Real period |
R |
4.9201991961092 |
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 |
33984bn1 1062i1 3776e1 |
Quadratic twists by: -4 8 -3 |