Atkin-Lehner |
2+ 3+ 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
72384a |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
6912 |
Modular degree for the optimal curve |
Δ |
-72384 = -1 · 26 · 3 · 13 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -2 4 13+ 5 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-21,-33] |
[a1,a2,a3,a4,a6] |
Generators |
[74:631:1] |
Generators of the group modulo torsion |
j |
-16777216/1131 |
j-invariant |
L |
4.7968120122615 |
L(r)(E,1)/r! |
Ω |
1.1064167604403 |
Real period |
R |
4.3354477119572 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994574 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
72384cs1 1131b1 |
Quadratic twists by: -4 8 |