Atkin-Lehner |
2+ 3- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
35136s |
Isogeny class |
Conductor |
35136 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-728580096 = -1 · 214 · 36 · 61 |
Discriminant |
Eigenvalues |
2+ 3- -3 -3 -1 -1 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,36,-1296] |
[a1,a2,a3,a4,a6] |
Generators |
[10:8:1] [18:-72:1] |
Generators of the group modulo torsion |
j |
432/61 |
j-invariant |
L |
6.8486711109911 |
L(r)(E,1)/r! |
Ω |
0.75811135082059 |
Real period |
R |
1.1292323851204 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999991 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
35136cf1 2196f1 3904a1 |
Quadratic twists by: -4 8 -3 |