The Securities and Exchange Commission is investigating whether Tesla CEO Elon Musk broke federal law on Tuesday when he tweeted about plans to take Tesla private at a price of $420 per share, The Wall Street Journal is reporting.

"Am considering taking Tesla private at $420," Musk tweeted on Tuesday. "Funding secured."

US law makes it a crime to "spread false or misleading information about a company" with the intent of manipulating its stock price, according to the SEC.

Musk's tweet certainly moved markets. Within minutes, the stock price rose from around $355 to nearly $370. It rose further later that day as Musk provided additional details about the plan. The stock ended Tuesday just under $380—up a total of 11 percent for the day. It fell to $370 on Wednesday.

The big question, of course, is whether Musk's tweet was accurate—particularly whether it's true that he has "funding secured." Musk hasn't specified who would fund his buyout plan, and so far, reporters trying to figure it out have come up empty-handed.

As we reported this morning in Pro Rata: Those not involved in Tesla financing include Apple, SoftBank, Uber, TPG, Silver Lake, Mubadala, KKR and basically every large Wall St bank. — Dan Primack (@danprimack) August 8, 2018

Securities lawyers were aghast at the haphazard way Musk announced his plans.

"A securities attorney would say 'what the hell are you doing?'" said University of Arizona legal scholar William Sjostrom in a Wednesday interview.

Companies usually halt trading of their stock before announcing big news so shareholders can't later file lawsuits claiming they traded on incomplete or misleading information. For the same reason, normal companies are careful to release the full details on a proposal like this all at once instead of dribbling the information out one tweet at a time.

But the most important question, Sjostrom said, is whether Musk's tweet is true or not. Sjostrom told Ars that if Musk's tweets are accurate—if Musk really has secured the necessary funding—then he's probably on solid legal footing.

"If everything he said is correct, the only question would be whether he didn't say enough, which is a harder case to bring," he said.

It's a little hard to believe a CEO would tweet "funding secured" if he didn't actually have funding secured. On the other hand, it's also a bit hard to imagine who would be willing and able to put up the tens of billions of dollars Musk would need to take Tesla private. And you'd think an entity putting up that kind of money would insist that Musk announce the move in a more conventional way to avoid unnecessary legal trouble.