Atkin-Lehner |
2+ 3- 5+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
42720b |
Isogeny class |
Conductor |
42720 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
40960 |
Modular degree for the optimal curve |
Δ |
180225000000 = 26 · 34 · 58 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 2 -4 4 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1986,-27936] |
[a1,a2,a3,a4,a6] |
Generators |
[-18:48:1] |
Generators of the group modulo torsion |
j |
13542540101056/2816015625 |
j-invariant |
L |
6.9932642155502 |
L(r)(E,1)/r! |
Ω |
0.72561154147363 |
Real period |
R |
2.4094380449573 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000005 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
42720f1 85440k1 128160bf1 |
Quadratic twists by: -4 8 -3 |