Atkin-Lehner |
2- 7+ 11- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
69454m |
Isogeny class |
Conductor |
69454 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
27349897272544 = 25 · 7 · 116 · 413 |
Discriminant |
Eigenvalues |
2- 1 -3 7+ 11- -2 3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-9622,-262844] |
[a1,a2,a3,a4,a6] |
Generators |
[-78:160:1] |
Generators of the group modulo torsion |
j |
55611739513/15438304 |
j-invariant |
L |
7.9494246892394 |
L(r)(E,1)/r! |
Ω |
0.49213799439292 |
Real period |
R |
1.6152836763433 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000915 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
574f1 |
Quadratic twists by: -11 |