Atkin-Lehner |
2+ 3+ 5- 7+ |
Signs for the Atkin-Lehner involutions |
Class |
47040z |
Isogeny class |
Conductor |
47040 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
-88510464000 = -1 · 215 · 32 · 53 · 74 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 7+ -5 -1 -8 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-65,14337] |
[a1,a2,a3,a4,a6] |
Generators |
[-23:56:1] [-16:105:1] |
Generators of the group modulo torsion |
j |
-392/1125 |
j-invariant |
L |
8.4284664689451 |
L(r)(E,1)/r! |
Ω |
0.86338481942137 |
Real period |
R |
0.13558500411135 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999985 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47040da1 23520bo1 47040cr1 |
Quadratic twists by: -4 8 -7 |