Judges and justices are supposed to be impartial arbiters of conflicting claims. Supreme Court Justice Samuel Alito is not. The New York Times reported that an upside-down flag flew in front of Justice Alito’s home after the 2020 election. That symbolism was adopted as a protest by Trump’s zealous and disappointed fans. Alito was one of them. He blamed his wife, as if he had no decisions about what flag was flying in his front yard. How can he be expected to rule impartially on cases about that election?

After the 2020 presidential election, as some Trump supporters falsely claimed that President Biden had stolen the office, many of them displayed a startling symbol outside their homes, on their cars and in online posts: an upside-down American flag.

One of the homes flying an inverted flag during that time was the residence of Supreme Court Justice Samuel A. Alito Jr., in Alexandria, Va., according to photographs and interviews with neighbors.

The upside-down flag was aloft on Jan. 17, 2021, the images showed. President Donald J. Trump’s supporters, including some brandishing the same symbol, had rioted at the Capitol a little over a week before. Mr. Biden’s inauguration was three days away. Alarmed neighbors snapped photographs, some of which were recently obtained by The New York Times. Word of the flag filtered back to the court, people who worked there said in interviews.

While the flag was up, the court was still contending with whether to hear a 2020 election case, with Justice Alito on the losing end of that decision. In coming weeks, the justices will rule on two climactic cases involving the storming of the Capitol on Jan. 6, including whether Mr. Trump has immunity for his actions. Their decisions will shape how accountable he can be held for trying to overturn the last presidential election and his chances for re-election in the upcoming one.

“I had no involvement whatsoever in the flying of the flag,” Justice Alito said in an emailed statement to The Times. “It was briefly placed by Mrs. Alito in response to a neighbor’s use of objectionable and personally insulting language on yard signs.”

Judicial experts said in interviews that the flag was a clear violation of ethics rules, which seek to avoid even the appearance of bias, and could sow doubt about Justice Alito’s impartiality in cases related to the election and the Capitol riot.