Atkin-Lehner |
7- 11+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
47971d |
Isogeny class |
Conductor |
47971 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
15360 |
Modular degree for the optimal curve |
Δ |
-115178371 = -1 · 76 · 11 · 89 |
Discriminant |
Eigenvalues |
0 -2 -3 7- 11+ 1 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,33,522] |
[a1,a2,a3,a4,a6] |
Generators |
[-54:45:8] [2:-25:1] |
Generators of the group modulo torsion |
j |
32768/979 |
j-invariant |
L |
4.181154011312 |
L(r)(E,1)/r! |
Ω |
1.4079838092739 |
Real period |
R |
0.74240093951596 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999979 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
979a1 |
Quadratic twists by: -7 |