Atkin-Lehner |
3- 7+ 11+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
36729m |
Isogeny class |
Conductor |
36729 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
492480 |
Modular degree for the optimal curve |
Δ |
-8059966464127347 = -1 · 315 · 73 · 11 · 533 |
Discriminant |
Eigenvalues |
2 3- 2 7+ 11+ 1 -4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-643809,-198877721] |
[a1,a2,a3,a4,a6] |
Generators |
[31142498044:-355698610457:31554496] |
Generators of the group modulo torsion |
j |
-40482499052479393792/11056195424043 |
j-invariant |
L |
12.714936563635 |
L(r)(E,1)/r! |
Ω |
0.084270036638172 |
Real period |
R |
12.573603729627 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12243b1 |
Quadratic twists by: -3 |