Atkin-Lehner |
3+ 5+ 19- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
84075c |
Isogeny class |
Conductor |
84075 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
110592 |
Modular degree for the optimal curve |
Δ |
-4268119921875 = -1 · 33 · 58 · 193 · 59 |
Discriminant |
Eigenvalues |
0 3+ 5+ 1 0 -5 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,2717,82218] |
[a1,a2,a3,a4,a6] |
Generators |
[-134:1421:8] [-12:218:1] |
Generators of the group modulo torsion |
j |
141909917696/273159675 |
j-invariant |
L |
8.0131865744983 |
L(r)(E,1)/r! |
Ω |
0.5363967013623 |
Real period |
R |
2.4898197403956 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000111 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
16815c1 |
Quadratic twists by: 5 |