Former President Donald J. Trump urged the Supreme Court on Thursday to reverse a ruling barring him from the primary ballot in Colorado and to declare him eligible to seek and hold the office of the presidency.

Mr. Trump’s brief, his main submission in an extraordinary case with the potential to alter the course of the presidential election, was a forceful recitation of more than half a dozen arguments about why the Colorado Supreme Court had gone astray in ruling him an insurrectionist barred from office by the Constitution.

“The court should put a swift and decisive end to these ballot-disqualification efforts, which threaten to disenfranchise tens of millions of Americans and which promise to unleash chaos and bedlam if other state courts and state officials follow Colorado’s lead and exclude the likely Republican presidential nominee from their ballots,” the brief said.

The case will be argued on Feb. 8, and the court will probably decide it quickly, perhaps by March 5, when many states, including Colorado, hold primaries.