Atkin-Lehner |
2- 3+ 13- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
8892f |
Isogeny class |
Conductor |
8892 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
8064 |
Modular degree for the optimal curve |
Δ |
-752750517168 = -1 · 24 · 33 · 136 · 192 |
Discriminant |
Eigenvalues |
2- 3+ -2 0 -2 13- 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1836,51569] |
[a1,a2,a3,a4,a6] |
Generators |
[-40:247:1] |
Generators of the group modulo torsion |
j |
-1584375054336/1742478049 |
j-invariant |
L |
3.6726674896489 |
L(r)(E,1)/r! |
Ω |
0.81625163270474 |
Real period |
R |
0.24996836096017 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
35568bf1 8892e1 115596g1 |
Quadratic twists by: -4 -3 13 |