Atkin-Lehner |
2- 3+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
27744r |
Isogeny class |
Conductor |
27744 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
36162326574144 = 26 · 34 · 178 |
Discriminant |
Eigenvalues |
2- 3+ -2 0 -4 -2 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-29574,1945944] |
[a1,a2,a3,a4,a6] |
Generators |
[-181:1156:1] [27:1080:1] |
Generators of the group modulo torsion |
j |
1851804352/23409 |
j-invariant |
L |
6.2208184038909 |
L(r)(E,1)/r! |
Ω |
0.65344801738275 |
Real period |
R |
9.5199897136533 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
27744z1 55488dp2 83232i1 1632l1 |
Quadratic twists by: -4 8 -3 17 |