Atkin-Lehner |
2- 5+ 7- 61- |
Signs for the Atkin-Lehner involutions |
Class |
8540d |
Isogeny class |
Conductor |
8540 |
Conductor |
∏ cp |
42 |
Product of Tamagawa factors cp |
deg |
16800 |
Modular degree for the optimal curve |
Δ |
321511187200 = 28 · 52 · 77 · 61 |
Discriminant |
Eigenvalues |
2- -1 5+ 7- -5 0 -7 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-10836,436936] |
[a1,a2,a3,a4,a6] |
Generators |
[6:610:1] [10:574:1] |
Generators of the group modulo torsion |
j |
549706426371664/1255903075 |
j-invariant |
L |
4.6898517810442 |
L(r)(E,1)/r! |
Ω |
0.9673575718408 |
Real period |
R |
0.11543108866291 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34160n1 76860s1 42700c1 59780j1 |
Quadratic twists by: -4 -3 5 -7 |