Atkin-Lehner |
3- 7+ 13- 31- |
Signs for the Atkin-Lehner involutions |
Class |
8463j |
Isogeny class |
Conductor |
8463 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
-21895651323 = -1 · 38 · 72 · 133 · 31 |
Discriminant |
Eigenvalues |
-2 3- -2 7+ -5 13- -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-8104,278206] |
[a1,a2,a3,a4,a6] |
Generators |
[-103:175:1] [5908864:21323858:148877] |
Generators of the group modulo torsion |
j |
-58867500778688512/21895651323 |
j-invariant |
L |
3.2330926280902 |
L(r)(E,1)/r! |
Ω |
1.185585490171 |
Real period |
R |
0.056812517508832 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999986 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25389i1 59241f1 110019w1 |
Quadratic twists by: -3 -7 13 |