Atkin-Lehner |
2- 3+ 5- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
68160cg |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
884736 |
Modular degree for the optimal curve |
Δ |
-3757206513600000000 = -1 · 212 · 38 · 58 · 713 |
Discriminant |
Eigenvalues |
2- 3+ 5- 0 2 4 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,342215,-52648775] |
[a1,a2,a3,a4,a6] |
Generators |
[395:12000:1] |
Generators of the group modulo torsion |
j |
1082080622856497984/917286746484375 |
j-invariant |
L |
6.5846547193896 |
L(r)(E,1)/r! |
Ω |
0.13727915760405 |
Real period |
R |
2.9978397823836 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000105 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68160dj1 34080m1 |
Quadratic twists by: -4 8 |