Atkin-Lehner |
2- 7+ 11+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
13706i |
Isogeny class |
Conductor |
13706 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
10752 |
Modular degree for the optimal curve |
Δ |
-135086336 = -1 · 28 · 72 · 112 · 89 |
Discriminant |
Eigenvalues |
2- -3 -3 7+ 11+ -4 -5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-219,1419] |
[a1,a2,a3,a4,a6] |
Generators |
[-13:50:1] [-11:54:1] |
Generators of the group modulo torsion |
j |
-1156633033473/135086336 |
j-invariant |
L |
5.2339285147143 |
L(r)(E,1)/r! |
Ω |
1.7934440506355 |
Real period |
R |
0.091198978873559 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
109648w1 123354p1 95942y1 |
Quadratic twists by: -4 -3 -7 |