Atkin-Lehner |
2- 3+ 5- 7+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
87360fa |
Isogeny class |
Conductor |
87360 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
-5009571840000 = -1 · 222 · 3 · 54 · 72 · 13 |
Discriminant |
Eigenvalues |
2- 3+ 5- 7+ -4 13+ -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,415,-107775] |
[a1,a2,a3,a4,a6] |
Generators |
[55:280:1] |
Generators of the group modulo torsion |
j |
30080231/19110000 |
j-invariant |
L |
4.6444887487629 |
L(r)(E,1)/r! |
Ω |
0.35872101003513 |
Real period |
R |
1.6184195438527 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002823 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
87360dn1 21840bu1 |
Quadratic twists by: -4 8 |