Musk's August 7 tweets helped push Tesla's stock price more than 13 percent above the prior day's close.
As a result, Tesla shares jumped 11 percent, causing so-called short-sellers who have been betting on the stock crashing for years to lose millions.
Musk had earlier discussed the prospect of taking the company private, with Saudi Arabia's sovereign wealth fund.
Elon Musk has a twenty percent stake of Tesla and he is the largest shareholder. Mr. Musk also said he had secured funding for the proposal, he provided no details.
Musk wrote "funding secured", and was considering to take Tesla private at $420 per share.
July 1, 2018 - Tesla factory workers produce more than 5,000 Model 3 sedans during the last week of June, hitting Musk's goal. In a letter to clients dated July 31, Einhorn said he was happy his Tesla lease had ended, citing issues with the car's touch screen and power windows.
Securities laws forbid market manipulation by corporate leaders who announce pending stock purchases or sales when they have no intention or no means of carrying them out.
The Wall Street regulator is reported to have asked Tesla why plans to go private were disclosed on the social media platform rather than in an official filing.
Tesla is facing a make-or-break moment in its eight-year history as a public company, as competition from European automakers is poised to intensify with new electric vehicles from Mercedes, Audi, BMW and other rivals.
The cases are Isaacs v Musk et al, U.S. District Court, Northern District of California, No. 18-04865; and Chamberlain v Tesla Inc et al in the same court, No. 18-04876.