SALT LAKE CITY -- Attorneys for a polygamous family made famous on a reality television show on Friday asked a Utah federal judge not to block their challenge of the state's bigamy law.

Kody Brown and wives Meri, Janelle, Christine and Robyn filed a lawsuit in Salt Lake City's U.S. District Court in July.

The stars of the TLC show "Sister Wives" contend the law is unconstitutional because it violates their right to privacy, prohibiting them from living together and criminalizing their private sexual relationships.

Under Utah law, people are guilty of bigamy if they have multiple marriage licenses, or if they cohabitate with another consenting adult in a marriage-like relationship.

Formerly of Lehi, Utah, the Browns and their 17 children moved to Nevada in January after police launched a bigamy investigation. The Browns said they practice polygamy as part of their religious beliefs.

U.S. District Judge Clark Waddoups heard oral arguments in the case Friday in Salt Lake City and took the matter under advisement. It is not known when he will rule.

For the case to go forward, the judge must decide that the Browns have been harmed by the bigamy law.

In court, the Browns' attorney, Jonathan Turley, said the family has suffered losses of income and has been forced to move out of state because they were under investigation for bigamy.

They also have suffered "reputational harm" because the law labels the family a "criminal association," Turley said.

Assistant Utah Attorney General Jerrold Jensen called the Browns' lawsuit "great TV drama," but said there is no real threat to the family, which has neither been arrested or charged with any crime.