Atkin-Lehner |
2- 5+ 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
39160o |
Isogeny class |
Conductor |
39160 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
68921600 = 28 · 52 · 112 · 89 |
Discriminant |
Eigenvalues |
2- -2 5+ 0 11- -4 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-756,7744] |
[a1,a2,a3,a4,a6] |
Generators |
[-28:88:1] [-6:110:1] |
Generators of the group modulo torsion |
j |
186906097744/269225 |
j-invariant |
L |
6.1058984630039 |
L(r)(E,1)/r! |
Ω |
1.9488794651713 |
Real period |
R |
0.7832575811027 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78320h1 |
Quadratic twists by: -4 |