The Supreme Court term that ended this summer delivered a number of big wins for traditional conservative causes. The court made it easier to challenge federal regulations. It made it harder to prosecute former presidents. And it delivered another decision that expanded the rights of gun enthusiasts.

Those rulings left no doubt that the court, with a six-justice supermajority that had already upended abortion rights and affirmative action, is the most ideologically conservative Supreme Court since the early 1930s.

Yet it is almost certainly not the most conservative federal court in the country.

About 1,000 miles away, in New Orleans, the U.S. Court of Appeals for the Fifth Circuit has turned its corner of the federal judiciary into a proving ground for some of the most aggressive conservative arguments in American law. Six of the 17 judges were nominated by former president Donald J. Trump, who has vowed to continue transforming the federal judiciary with further nominations if elected again in November.

In a few of the biggest Supreme Court decisions of the last few years — including Dobbs v. Jackson, which ended a 49-year right to abortion — it was the Fifth Circuit that first ruled on the case, teeing it up for Supreme Court review and a seismic moment in American law and politics. And in the Supreme Court’s upcoming term, which begins in early October, the justices have agreed to hear five more cases from the Fifth Circuit, including a challenge to regulating so-called ghost guns.

The court’s jurisprudence has been so audacious that, in more than a few cases, its rulings have received a skeptical, even hostile response from the Supreme Court, which overruled the Fifth Circuit seven times just in this past term, on an array of disputes ranging from gun rights for domestic abusers, government regulation of social media, and the F.D.A.’s approval of an abortion drug.