The Supreme Court’s rejection Thursday of President-elect Donald J. Trump’s request to be spared conviction on 34 felony counts was just a few lines long and contained modest and practical arguments.

He remains free to appeal his conviction on the charge of falsifying business records, the court’s unsigned order said, and appearing by video without specific punishment in a New York court would pose a relatively insignificant burden.

More striking than the majority’s reasoning was the 5-4 vote in this case, which provided a vivid and telling picture of how the court is preparing for a second Trump administration and the flood of litigation that is sure to follow.

It was no surprise that the court’s three Democratic nominees — Justices Sonia Sotomayor, Elena Kagan and Ketanji Brown Jackson — were in the majority. After all, they had expressed bitter opinions when the court’s six Republican nominees granted Mr. Trump broad immunity in July from federal charges that he tried to undermine the 2020 election.

That ruling effectively killed the case and raised concerns that the court would not act as a check on Mr. Trump if he returned to the White House. Those concerns were heightened by news that Justice Samuel A. Alito Jr. consulted with Mr. Trump by telephone on Tuesday.

If the votes of the three liberal justices were predictable, those of the court’s two conservative members who voted with them Thursday — Chief Justice John G. Roberts Jr. and Justice Amy Coney Barrett — were more surprising.

The chief justice was the author not only of the immunity decision but also of the majority opinions in two other victories for Mr. Trump last term, one of which cast doubt on some of the federal charges against him and the other of which allowed him to remain in office despite another term to seek another term in office. Constitutional provision prohibiting insurgents from holding office.

These three rulings, the last of which was unsigned but was clearly a product of Roberts, undermined the reputation he had built over nearly two decades as an institutionalist who sought to defend his court against accusations that it had been corrupted by the Politics distorted.

His vote Thursday aligned with veteran Chief Justice Roberts, who in 2012 cast the deciding vote to uphold the Affordable Care Act, President Barack Obama’s most significant legislative achievement, and the one who rebuked Mr. Trump as he sought a federal judgeship , who decided against his government’s asylum policy.

“We have no Obama judges, no Trump judges, no Bush judges or Clinton judges,” Chief Justice Roberts said in a statement in 2018. “We have an exceptional group of dedicated judges who do their best to serve everyone , who appear to give the same right.” in front of them. We should all be grateful for this independent judiciary.”

For his part, Mr. Trump has long been a critic of the chief justice. After the Affordable Care Act decision, Mr. Trump wrote on Twitter: “I guess @JusticeRoberts wanted to be a part of Georgetown society more than anyone knew,” citing a fake name. During his first presidential campaign, Mr. Trump called the chief justice “an absolute disaster.”

The court’s three liberals had to do more than just win the chief justice’s vote to prevail. These days, their most promising potential conservative ally is Judge Barrett, whom Mr. Trump put on the court just weeks before his 2020 election defeat.

Judge Barrett, in standard journalistic terms, has an independent streak that she displayed in all three Trump cases last term. In each of them she clashed with the Chief Justice.

She authored a remarkable dissent, joined by liberal justices, against a decision that limited the tools prosecutors can use in cases against members of the Jan. 6 mob. And she voted with the court’s three-judge liberal wing in March, saying the majority had overreached in reinstating former President Donald J. Trump in Colorado.

In deciding to grant Mr. Trump significant immunity from prosecution, Justice Barrett wrote a concurring opinion in which he proposed a different framework than that laid out by Chief Justice Roberts in the majority opinion. She said Mr. Trump’s efforts to organize alternative voter slates were “not entitled to protection,” adding that she agreed with the disagreement over how evidence could be used in the case.

Overall, Judge Barrett was the Republican nominee most likely to vote for a liberal outcome in the last legislative session. On Thursday, she joined Chief Justice Roberts in denying an urgent request from the new president.

A snapshot is just a moment in time and it does not predict what the future will bring. However, there is reason to believe that not everything will be smooth sailing for Mr. Trump.

In his first term, he performed poorly before the Supreme Court on signed decisions in oral cases in which the United States, an executive branch, an independent agency, or the president himself was a party, prevailing only 42 percent of the time , which represented the lowest rate since at least the Franklin D. Roosevelt administration.

In other words, a fundamentally conservative court that now has a six-justice majority among Republican nominees, including three appointed by Mr. Trump himself, was not particularly receptive to his arguments. In contrast, the Biden administration was on the winning side54 percent of the time.

Mr. Trump has repaid this track record with bitterness. “I am not happy with the Supreme Court,” he said during his speech at the White House on January 6, 2021. “They love to rule against me.”

He spoke ruefully about his three appointees, Barrett, Neil M. Gorsuch and Brett M. Kavanaugh, suggesting that they had betrayed him to ensure their independence.

“I picked three people,” he said. “I fought like hell for her.”

On Thursday, Justices Gorsuch and Kavanaugh noted that they disagreed with the order that Mr. Trump appear for his sentencing. The same was true for the court’s two most conservative members, Justices Clarence Thomas and Samuel A. Alito Jr. None of the four gave reasons.

In a statement on Wednesday, Justice Alito said he had spoken to Mr. Trump on the phone and given him a recommendation for a former employee. He said they did not discuss pending or upcoming cases and he did not recuse himself from the sentencing issue.