Atkin-Lehner |
2+ 7+ 17+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
68306a |
Isogeny class |
Conductor |
68306 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
591360 |
Modular degree for the optimal curve |
Δ |
-1107716589022148 = -1 · 22 · 78 · 17 · 414 |
Discriminant |
Eigenvalues |
2+ -3 -2 7+ -3 -3 17+ 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,9497,1558801] |
[a1,a2,a3,a4,a6] |
Generators |
[80:-1721:1] |
Generators of the group modulo torsion |
j |
16431340023/192151748 |
j-invariant |
L |
1.8814499847472 |
L(r)(E,1)/r! |
Ω |
0.3612702658735 |
Real period |
R |
1.3019684717913 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004759 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68306r1 |
Quadratic twists by: -7 |