Atkin-Lehner |
3- 5+ 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
84825o |
Isogeny class |
Conductor |
84825 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
331776 |
Modular degree for the optimal curve |
Δ |
-188410904296875 = -1 · 39 · 59 · 132 · 29 |
Discriminant |
Eigenvalues |
-2 3- 5+ 0 3 13+ -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-75,660406] |
[a1,a2,a3,a4,a6] |
Generators |
[-86:175:1] [130:1687:1] |
Generators of the group modulo torsion |
j |
-4096/16540875 |
j-invariant |
L |
6.0815042894305 |
L(r)(E,1)/r! |
Ω |
0.45122919128085 |
Real period |
R |
0.42117622865863 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000018 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
28275e1 16965j1 |
Quadratic twists by: -3 5 |