Atkin-Lehner |
2+ 3+ 5- 71- |
Signs for the Atkin-Lehner involutions |
Class |
68160r |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
153600 |
Modular degree for the optimal curve |
Δ |
-127800000 = -1 · 26 · 32 · 55 · 71 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 3 2 1 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-146895,21719025] |
[a1,a2,a3,a4,a6] |
Generators |
[1770:75:8] |
Generators of the group modulo torsion |
j |
-5477315219811126784/1996875 |
j-invariant |
L |
7.3076393485064 |
L(r)(E,1)/r! |
Ω |
1.1115819845827 |
Real period |
R |
0.65740894060772 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995554 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68160bk1 34080be1 |
Quadratic twists by: -4 8 |