Atkin-Lehner |
2- 3+ 7- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
84084g |
Isogeny class |
Conductor |
84084 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
580608 |
Modular degree for the optimal curve |
Δ |
-11846186792504064 = -1 · 28 · 36 · 79 · 112 · 13 |
Discriminant |
Eigenvalues |
2- 3+ 3 7- 11+ 13+ 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,45211,-3720639] |
[a1,a2,a3,a4,a6] |
Generators |
[355:7546:1] |
Generators of the group modulo torsion |
j |
339326861312/393323931 |
j-invariant |
L |
6.865271379059 |
L(r)(E,1)/r! |
Ω |
0.21623213236911 |
Real period |
R |
0.66144881190081 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000937 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12012g1 |
Quadratic twists by: -7 |