Shares of gene sequencing leader Illumina (ILMN 1.02%) rallied 36.6% in December, according to data from S&P Global Market Intelligence.

Investors might not be quite so excited, as Illumina entered the month more than 80% below its all-time highs from 2021.

But hopes for a bottoming and recovery surfaced in December, as Illumina received several positive analyst notes, and activist investor Carl Icahn made his next move in shaking up the company's board of directors.

Is the company at the start of its recovery?

Wall Street analysts are generally mixed on Illumina, with some downgrading shares last month. Yet the two firms that initiated coverage on the name, taking a look with fresh eyes, were bullish. Both Wolfe Research and Stephens initiated coverage on Illumina with buy ratings and $175 and $170 price targets, respectively.

Wolfe Research sees three steps to "material upside" in Illumina shares, including divesting Grail as soon as possible, demonstrating more "elasticity" in its products (demand rising as prices come down), and new financial discipline under new CEO Jacob Thaysen, who was just appointed on Sept. 25. Similarly, Stephens likes Illumina when looking past short-term troubles and taking a "longer-term view." The Stephens analysts still believe Illumina has the best and most complete portfolio of gene sequencing products, despite some rising competition from Chinese players.

To be clear, Illumina is still dealing with significant issues. Illumina purchased cancer detection diagnostic company Grail for $7.1 billion in July 2021 despite European regulators not having signed off on the deal. So European Union regulators launched an investigation, and the U.S. Federal Trade Commission opened a case shortly thereafter to undo the deal, citing similar anticompetitive concerns. The acquisition and stock price decline also attracted activist investor Carl Icahn, who thought the acquisition of the loss-making Grail was a breach of fiduciary duty.

In July, Illumina was fined $476 million by the E.U., and was then ordered by authorities to divest Grail in October. In December, a U.S. appeals court struck down the FTC's suit against Illumina, but only on the basis of the wrong legal standard. In the ruling, the appeals court actually noted the FTC had extensive evidence that the acquisition would harm competition.

So, Illumina confirmed in December that it would sell Grail. While we don't know yet at what price the company will sell the asset, it's likely to be well below what it paid for it. Still, a cash infusion would be a relief for some shareholders who believe Illumina should stick with its core business.

Icahn is certainly one of those investors. While he was successful in ousting Illumina's former CEO and former chairman as the result of a proxy fight earlier this year, Icahn sent yet another letter calling for the removal of Illumina's "legacy" directors in December. Icahn is attempting to remove anyone who had authority during the decision to purchase Grail. So having an activist on the case to further "clean up" perceived wrongs at the company was welcomed by investors.

"We believe that, without the influence of the legacy directors, CEO Jacob Thaysen, the new directors and Illumina's employees will restore Illumina back to the great company it once was and can be again," Icahn wrote.

Illumina is down, but is it cheap?

While Illumina's overall business is suffering from headline losses, the core business did generate about $250 million of non-GAAP (adjusted) operating income last quarter. That's a billion-dollar run rate, but growth has also stagnated in recent years, which perhaps explains the need to acquire Grail.

Illumina currently has a $21 billion market cap, or about 21 times its run rate pre-tax earnings. That's actually not especially cheap for a company with little growth. However, the genetic testing industry is still in early days. So if Illumina's new CEO can engineer a resumption of growth, the stock could be interesting. But it's clearly still a risky name.