Atkin-Lehner |
2+ 3+ 5- 71- |
Signs for the Atkin-Lehner involutions |
Class |
68160o |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-65433600 = -1 · 212 · 32 · 52 · 71 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 0 2 -2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,55,-375] |
[a1,a2,a3,a4,a6] |
Generators |
[15:60:1] |
Generators of the group modulo torsion |
j |
4410944/15975 |
j-invariant |
L |
5.9614296513779 |
L(r)(E,1)/r! |
Ω |
0.99700624057853 |
Real period |
R |
1.4948325818708 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000665 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68160bg1 34080bd1 |
Quadratic twists by: -4 8 |