Elephas has the highest base Special Defense stat of all non-legendary Normal-type Pokémon. It is also mentioned multiple times in Pokédex entries of Pokémon such as Deloris or Yedoom.
At one point during development Elephas was supposed to have a cross-generational evolution named Mammudha.
This Pokemon is the butt of jokes most of the time, being referred to an Indian Elephant. For example, Frutagon's description states that it cut 665 Elephases in one slash, and Farfigtron's description states that its fire can melt Elephases.
Elephas' concept predicted the official Pokémon Copperajah, which is also based on an Indian elephant.
Its shiny is most likely based on the fact that elephants in drawings and cartoons are commonly blue.
Elephas is literally an Indian elephant, and its design references several stereotypes pertaining to Indian people. It is designed as a joke and reference towards the perplexing fact that Raichu and Gastly's Pokédex entries mention said animal.
Its Dex Entry lampshades this by mentioning how it can withstand electricity and is afraid of ghosts.
Despite this, Electric attacks affect it normally and it's immune to Ghost-type attacks.
Literally elephas, the scientific classification of an Asian elephant.