Atkin-Lehner |
7+ 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
47971b |
Isogeny class |
Conductor |
47971 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
25704 |
Modular degree for the optimal curve |
Δ |
-5643740179 = -1 · 78 · 11 · 89 |
Discriminant |
Eigenvalues |
0 0 3 7+ 11- -6 -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-686,7803] |
[a1,a2,a3,a4,a6] |
Generators |
[-27:81:1] |
Generators of the group modulo torsion |
j |
-6193152/979 |
j-invariant |
L |
4.9404723502812 |
L(r)(E,1)/r! |
Ω |
1.3040633481526 |
Real period |
R |
3.7885217441733 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000052 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47971h1 |
Quadratic twists by: -7 |