Atkin-Lehner |
3- 5+ 7+ 83+ |
Signs for the Atkin-Lehner involutions |
Class |
61005m |
Isogeny class |
Conductor |
61005 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
-218006758816875 = -1 · 36 · 54 · 78 · 83 |
Discriminant |
Eigenvalues |
-2 3- 5+ 7+ -3 2 -2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,12234,487190] |
[a1,a2,a3,a4,a6] |
Generators |
[-36:37:1] [114:1837:1] |
Generators of the group modulo torsion |
j |
35124432896/37816875 |
j-invariant |
L |
6.1049960158863 |
L(r)(E,1)/r! |
Ω |
0.37174839241214 |
Real period |
R |
0.45617742033306 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999986 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61005l1 |
Quadratic twists by: -7 |