Basils swam like a serpent, side to side movement of the tail, not the up and down movement of whales and dolphins.
Untrue. Wikipedia:
"It is also believed to have rather unique locomotion compared with all other cetaceans; similarly sized thoracic, lumbar, sacral and causal vertebrae imply that Basilosaurus moved in an anguilliform (eel-like) fashion,
only vertically. Even more oddly, paleontologist Philip Gingerich theorized that is may also move in a horizontal anguilliform fashion to some degree, something completely unknown in cetaceans. The skeletal anatomy of the tail suggests that a small fluke was probably present, which would have only aided vertical motion. Most reconstructions show a small, speculative dorsal fin similar to a rorqual whale's, but other reconstructions show a dorsal ridge."
My emphasis.
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