Atkin-Lehner |
2+ 7+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
20384b |
Isogeny class |
Conductor |
20384 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
10368 |
Modular degree for the optimal curve |
Δ |
-127848448 = -1 · 212 · 74 · 13 |
Discriminant |
Eigenvalues |
2+ -2 -4 7+ -5 13- 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-65,559] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:8:1] [-5:28:1] |
Generators of the group modulo torsion |
j |
-3136/13 |
j-invariant |
L |
4.1699001012913 |
L(r)(E,1)/r! |
Ω |
1.6156542562865 |
Real period |
R |
0.21507799317556 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999991 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
20384a1 40768ca1 20384j1 |
Quadratic twists by: -4 8 -7 |