Atkin-Lehner |
2+ 3+ 5+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
68160f |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
235192896000000 = 212 · 36 · 56 · 712 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 -4 -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-15721,-171479] |
[a1,a2,a3,a4,a6] |
Generators |
[-111:440:1] [-65:756:1] |
Generators of the group modulo torsion |
j |
104913624746944/57420140625 |
j-invariant |
L |
8.2254552339514 |
L(r)(E,1)/r! |
Ω |
0.45546625428576 |
Real period |
R |
9.0297087397095 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000021 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
68160u2 34080bi1 |
Quadratic twists by: -4 8 |