Atkin-Lehner |
2+ 3- 19+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
121752i |
Isogeny class |
Conductor |
121752 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-177514416 = -1 · 24 · 38 · 19 · 89 |
Discriminant |
Eigenvalues |
2+ 3- -3 -2 -3 -3 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,6,641] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:9:1] [4:-27:1] |
Generators of the group modulo torsion |
j |
2048/15219 |
j-invariant |
L |
8.5299549929797 |
L(r)(E,1)/r! |
Ω |
1.4207113155207 |
Real period |
R |
0.75050037412852 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000002772 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40584q1 |
Quadratic twists by: -3 |