Atkin-Lehner |
2+ 3- 5+ 13- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
47970k |
Isogeny class |
Conductor |
47970 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
-443903059080000 = -1 · 26 · 36 · 54 · 135 · 41 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 2 13- 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,9495,946701] |
[a1,a2,a3,a4,a6] |
Generators |
[58:-1329:1] |
Generators of the group modulo torsion |
j |
129854009067119/608920520000 |
j-invariant |
L |
3.6911823087804 |
L(r)(E,1)/r! |
Ω |
0.379100737178 |
Real period |
R |
0.48683396611948 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999912 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5330h1 |
Quadratic twists by: -3 |