Atkin-Lehner |
2- 3+ 5- 7- 89- |
Signs for the Atkin-Lehner involutions |
Class |
18690m |
Isogeny class |
Conductor |
18690 |
Conductor |
∏ cp |
512 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
192320100000000 = 28 · 32 · 58 · 74 · 89 |
Discriminant |
Eigenvalues |
2- 3+ 5- 7- -4 -2 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-43400,3397385] |
[a1,a2,a3,a4,a6] |
Generators |
[-187:2333:1] |
Generators of the group modulo torsion |
j |
9040522389540969601/192320100000000 |
j-invariant |
L |
6.9409383933161 |
L(r)(E,1)/r! |
Ω |
0.56623292571878 |
Real period |
R |
1.5322621835584 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
8 |
Number of elements in the torsion subgroup |
Twists |
56070l1 93450bc1 |
Quadratic twists by: -3 5 |