Atkin-Lehner |
2- 3+ 29- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
84912p |
Isogeny class |
Conductor |
84912 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
179712 |
Modular degree for the optimal curve |
Δ |
-119943044739072 = -1 · 212 · 39 · 293 · 61 |
Discriminant |
Eigenvalues |
2- 3+ 0 2 2 1 4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,11392,-245952] |
[a1,a2,a3,a4,a6] |
Generators |
[144:2088:1] |
Generators of the group modulo torsion |
j |
39914029109375/29282969907 |
j-invariant |
L |
6.8170562004943 |
L(r)(E,1)/r! |
Ω |
0.33055363422364 |
Real period |
R |
1.7185955864616 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999972235 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5307b1 |
Quadratic twists by: -4 |