She and Giannulli waived their right to appear in federal court in Boston for arraignment as they filed not-guilty pleas Monday through signed statements. Prosecutors allege that the couple paid a total of $500,000 to facilitate admission of their daughters to USC as purported crew recruits.

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An attorney for the couple declined to comment Monday.

They are among 33 parents who prosecutors say paid bribes to help get their children into prominent universities in a scheme orchestrated by admission consultant William “Rick” Singer. Some paid to obtain fraudulent scores on the ACT or SAT tests, prosecutors allege, while others paid to have their children designated as recruited athletes even though they lacked credentials to compete at the intercollegiate level.

Singer has pleaded guilty to racketeering conspiracy and other crimes and is cooperating in the case.

Among the accused parents who were his clients, 13 agreed last week to plead guilty to conspiring to commit mail fraud and honest services mail fraud, prosecutors say. Those defendants, including actress Felicity Huffman of Los Angeles, are scheduled to appear for plea hearings next month in U.S. District Court in Boston. It is not clear what penalty they will face. The fraud-conspiracy charge carries a maximum sentence of 20 years in prison and substantial fines. (One of the 13 also agreed to plead guilty to money laundering conspiracy.)

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Others are fighting the allegations in a case that could hinge on whether payments the parents made are judged to have been bribes or simply contributions to university athletic programs and a charity Singer controlled.

Court documents show at least eight others in addition to Loughlin and Giannulli have filed pleas of not guilty in recent days: Gamal Abdelaziz of Las Vegas; I-Hsin “Joey” Chen of Newport Beach, Calif.; Amy Colburn and Gregory Colburn of Palo Alto, Calif.; Michelle Janavs of Newport Coast, Calif.; Elisabeth Kimmel of Las Vegas; David Sidoo of Vancouver; and Robert Zangrillo of Miami.

In all, 50 people were charged in the case. The accusations, made public last month, have raised questions about equity in admissions to prominent colleges and universities.

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The undergraduate admission rate at USC is now about 11 percent, according to the university, and it has been falling in recent years as application totals have grown. Court documents show that parents were mindful of fierce competition. In April 2016, Giannulli copied Loughlin on an email to Singer, according to an indictment: “I have some concerns and want to fully understand the game plan and make sure we have a roadmap for success as it relates to [our older daughter].”

Singer responded: “If you want [U]SC I have the game plan ready to go into motion. Call me to discuss.”

Jennifer Jenkins contributed to this report.