Atkin-Lehner |
2- 3+ 5- 71+ |
Signs for the Atkin-Lehner involutions |
Class |
68160ck |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
737280 |
Modular degree for the optimal curve |
Δ |
-18633240000000000 = -1 · 212 · 38 · 510 · 71 |
Discriminant |
Eigenvalues |
2- 3+ 5- 2 -2 -2 -4 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-674905,-213284903] |
[a1,a2,a3,a4,a6] |
Generators |
[1449:43000:1] |
Generators of the group modulo torsion |
j |
-8300272382462293696/4549130859375 |
j-invariant |
L |
5.2335492294674 |
L(r)(E,1)/r! |
Ω |
0.083280738470333 |
Real period |
R |
3.1421126450318 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001458 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68160dp1 34080n1 |
Quadratic twists by: -4 8 |