Rojas' La Celestina is about a "procuress" that one major character, Calisto, goes to when Melibea rejects his declaration of love—a natural step in courtly love.
Celestina decides to fleece Calisto out of as much money as possible as he attempts to make progress with Melibea. Ultimately Celestina makes some headway with Melibea, and Calisto give her a gold necklace as payment. Celestina does not share this with her "partners in crime," and they kill her. Calisto accidentally falls from a ladder, and Melibea throws herself off of a tower having seen Calisto die.
Petrarch had a reputation of a poet who was lovesick for a woman he could not have—Laura. He wrote over three hundred sonnets dedicated to her. However, it is noted that Roja's work seems not to refer to these sonnets.
It is generally accepted, on the basis of evidence presented by the two principal studies of the sources of La Celestina, that the influence of Petrarch upon Fernando de Rojas comes exclusively from the Latin prose works.
So, rather than being influenced by Petrarch's love poetry about Laura, Rojas was more influenced by Petrarch's earlier work.
[Castro] Guisasola notes that he found no mention of Petrarch's love poetry, "Latin or vernacular" except for...
...allusions to notable events mentioned, indeed, in the Trionfi, but which might have come from numerous other works...
Guisasola assumes, then, that the references of...
Petrarch encountered in La Celestina is not at all the anguished poet of love [from the Laura poems] whom we know today, but rather the illustrious humanist famous for his historical and moral treatises.
Petrarch had an early experience studying the law, which he did not care for. Clerical jobs made it possible for him to work on his writing. He was, in later years, named poet laureate, and ambassador. He collected old Latin papers, falling to ruin, and was very active in...
...the recovery of knowledge from writers of Rome and Greece.
Much of his work was done in Latin...as Petrarch was "an enthusiastic Latin scholar..."
His Latin writings include scholarly works, introspective essays, letters, and more poetry.
The sonnets for which he is so known for obviously were not the focus of Rojas' interest in Petrarch, but the other works he concentrated upon, which had nothing to do with his unrequited love of Laura, recounted in his "Laura poems."