Atkin-Lehner |
2- 3+ 5+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
68160ca |
Isogeny class |
Conductor |
68160 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
589824 |
Modular degree for the optimal curve |
Δ |
-84801945600000000 = -1 · 222 · 36 · 58 · 71 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 0 0 6 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,15679,13985121] |
[a1,a2,a3,a4,a6] |
Generators |
[839:24840:1] |
Generators of the group modulo torsion |
j |
1625964918479/323493750000 |
j-invariant |
L |
4.8233950481975 |
L(r)(E,1)/r! |
Ω |
0.26343838253486 |
Real period |
R |
4.5773465145733 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995738 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
68160t1 17040z1 |
Quadratic twists by: -4 8 |