Atkin-Lehner |
2- 3+ 7+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
108192y |
Isogeny class |
Conductor |
108192 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
-678580224 = -1 · 212 · 3 · 74 · 23 |
Discriminant |
Eigenvalues |
2- 3+ -1 7+ -6 -1 3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-30641,2074689] |
[a1,a2,a3,a4,a6] |
Generators |
[-135:1932:1] [103:28:1] |
Generators of the group modulo torsion |
j |
-323515119424/69 |
j-invariant |
L |
8.9269821588973 |
L(r)(E,1)/r! |
Ω |
1.2788861493638 |
Real period |
R |
0.58168991836225 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000001211 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
108192o1 108192br1 |
Quadratic twists by: -4 -7 |