Atkin-Lehner |
2+ 3+ 7- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
81984k |
Isogeny class |
Conductor |
81984 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
-8823464835591168 = -1 · 210 · 39 · 76 · 612 |
Discriminant |
Eigenvalues |
2+ 3+ 0 7- 0 -2 -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1653,-4518891] |
[a1,a2,a3,a4,a6] |
j |
-488095744000/8616664878507 |
j-invariant |
L |
1.1262519942228 |
L(r)(E,1)/r! |
Ω |
0.18770868127943 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
81984cf1 5124c1 |
Quadratic twists by: -4 8 |