What a beauty Fernando!!! Merry Christmas
These are I believe generally termed swept hilt rapiers, although with these heavier blades were more arming swords with military application. I think your date range is pretty well placed, and I would consider 17th century quite likely. The faceted bulbous pommel corresponds closely to an English type of c. 1630's (#77, A.V.B.Norman).
The markings are difficult to see clearly as the contrast between the bright cleaned area and age pitting have obscured the definition, but the parallel sickle marks with the well known three dots are clear, as observed by David.
This assymetrical hilt style is essentially Italian, and is seen on numbers of variants which include early styles of schiavona. I have a schiavona which has this distinct assymetric form in the hilt, and actually dates end of the 18th century, the tradition carried forward.
Norman notes that the style was during 16th century, but was present as early as late 15th.....with revival in the 17th.
To me these markings in an unusual completely parallel rather than opposed configuration suggest this blade is likely Italian and 17th century, probably early, rather than the Styrian blades often with 'sickle' marks and later.
The wider scope of variation in my opinion indicates the actual application of these as used by bladesmiths in compliance with guild ordinances, than the more familiar pattern of sickle marks applied spuriously on trade blades.
Congratulations Fernando on your new adoption!!!
All best regards,
Jim