Atkin-Lehner |
2+ 3- 5- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
68160bf |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-163584000000 = -1 · 214 · 32 · 56 · 71 |
Discriminant |
Eigenvalues |
2+ 3- 5- 0 0 0 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1905,-38097] |
[a1,a2,a3,a4,a6] |
Generators |
[101:900:1] |
Generators of the group modulo torsion |
j |
-46689225424/9984375 |
j-invariant |
L |
8.6076672759807 |
L(r)(E,1)/r! |
Ω |
0.35721906705375 |
Real period |
R |
2.0080272092886 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000155 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68160cr1 8520a1 |
Quadratic twists by: -4 8 |