Atkin-Lehner |
2- 3- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
27072cd |
Isogeny class |
Conductor |
27072 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
-2979958905372672 = -1 · 230 · 310 · 47 |
Discriminant |
Eigenvalues |
2- 3- 2 0 0 -2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,33396,-1174768] |
[a1,a2,a3,a4,a6] |
Generators |
[4141:266733:1] |
Generators of the group modulo torsion |
j |
21554582687/15593472 |
j-invariant |
L |
6.234961599658 |
L(r)(E,1)/r! |
Ω |
0.25337374021333 |
Real period |
R |
6.1519413914089 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
27072bc1 6768o1 9024bm1 |
Quadratic twists by: -4 8 -3 |