Atkin-Lehner |
2- 3- 7+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
81984cf |
Isogeny class |
Conductor |
81984 |
Conductor |
∏ cp |
72 |
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] |
Generators |
[75:2196:1] |
Generators of the group modulo torsion |
j |
-488095744000/8616664878507 |
j-invariant |
L |
6.7967425520789 |
L(r)(E,1)/r! |
Ω |
0.32917749695781 |
Real period |
R |
1.1470918025364 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002889 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
81984k1 20496h1 |
Quadratic twists by: -4 8 |