The Winkelvoss twins, the Harvard classmates of Mark Zuckerberg, have decided to call an end to their legal campaign against Facebook, dropping their promised appeal to the Supreme Court, in order to be content with the $65 million settlement they agreed to and then bitterly contested.

The former Olympic rowers told a California appeals court Wednesday that they would not be asking the Supreme Court to overturn that court’s ruling. The appeals court found that Facebook did not deceive the twins when the parties settled a lawsuit that alleged Mark Zuckerberg stole the idea for Facebook when he agreed to help the twins with their social networking site — without ever delivering on it.

Or in the legalese of the filing:

Appellants and Intervenors Cameron Winklevoss, Tyler Winklevoss and Divya Narendra hereby provide notice that after careful consideration, they have determined that they will not file a petition for a writ of certiorari in the United States Supreme Court in the above entitled case. Given this, and given that this Court’s decision to stay issuance of the mandate in the above-captioned case was premised upon the possibility of further appellate review, Appellants no longer oppose issuance of the mandate, and have no objection to vacatur of the stay of issuance of mandate.

The duo sued in 2004, alleging that Zuckerberg agreed to help the twins with their social network project, only to slowroll them and launch his own project instead. After mediation, the parties agreed to trade $20 million cash and more than a million Facebook shares for the Winklevoss twins’ company ConnectU.

The litigation, which played a central role in the hit 2010 film The Social Network, continued when the twins alleged that Facebook had deceived them about the value of the shares and that they were entitled to four times as many shares. A district court ruled in 2008 that the settlement should stand.

The U.S. 9th Circuit of Appeals agreed Monday (.pdf) that the Harvard grad twins weren’t dumb or badly represented, and that the whole sideshow ought to end.

That’s a fancy way of saying that the Winklevosses seemed to have finally heard the words written by the Ninth Circuit Court of Appeals Chief Judge Alex Kozinski wrote in April, when the appeals court told them to get over it.

“The Winklevosses are sophisticated parties who were locked in a contentious struggle over ownership rights in one of the world’s fastest-growing companies,” Kozinski wrote. “They engaged in discovery, which gave them access to a good deal of information about their opponents. They brought half-a-dozen lawyers to the mediation. Howard Winklevoss — father of Cameron and Tyler, former accounting professor at Wharton School of Business and an expert in valuation — also participated. A party seeking to rescind a settlement agreement [...] under these circumstances faces a steep uphill battle.

“With the help of a team of lawyers and a financial advisory, they made a deal that appears quite favorable in light of recent market activity,” Kozinski wrote, noting that the value of the shares the twins own has continued to grow in value as investors are putting money into Facebook at a $50 billion valuation. “For whatever reason, they now want to back out. Like the district court, we see no basis for allowing them to do so. At some point, litigation must come to an end. That point has now been reached.”

The twins argued that Facebook deceived them about the valuation of the company, handing them shares based on the $32 valuation that Microsoft invested in Facebook at, without telling them that an independent auditor valued the shares at less than $9 for purposes of handing out stock options to new employees (a common, if sketchy, practice in Silicon Valley).

When they learned of that, the twins filed suit to overturn the settlement, on the grounds they were entitled to four times as many shares. In the meantime, Facebook’s valuation — and thus the value of the settlement — has continued to grow — with Facebook now reportedly seeking a $100 billion IPO valuation.

Perhaps the idea of now having $200 million to split (minus the legal fees) convinced the twins to drop their pledge to go all the way to the Supreme Court. It’s not the ending that Aaron Sorkin would have written, but it’s the ending we got — just as Zuckerberg’s Facebook is the social network we got — not the one that lived in the heads of the Winklevoss twins back in 2003.

Photo: USA’s Cameron Winklevoss, left, and twin brother Tyler take the start of their Men’s pair repechage at the Beijing 2008 Olympics in Beijing, Monday, Aug. 11, 2008. Gregory Bull/AP