Defense attorneys asked a federal judge Tuesday to grant a new trial to the Mexican drug lord known as "El Chapo," saying jurors improperly followed media coverage of the sensational drug conspiracy case. Joaquin Guzman's defense team said in court filings that jurors repeatedly disregarded instructions to avoid the "blizzard of media coverage" before convicting Guzman of murder conspiracy and drug-trafficking charges in February.

The defense asked U.S. District Judge Brian Cogan to hold an evidentiary hearing in the wake of a Vice News report that said at least five jurors followed media reports and Twitter feeds during the three-month trial. The attorneys said juror misconduct denied Guzman his right to a fair trial.

"If a justice system's measure is how it treats the most reviled and unpopular, then ours may have failed Joaquin Guzman by denying him the fair trial before an untainted jury to which he's constitutionally entitled," Guzman's attorneys wrote in a court filing. "Because sunlight is the best disinfectant, that prospect merits serious consideration, close investigation and a new trial as appropriate."

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A spokesman for the U.S. attorney's office in Brooklyn declined to comment. The defense motion claims jurors "actively sought out and openly discussed" sensational allegations that had been excluded from Guzman's proceedings, including a claim by a government witness that Guzman raped girls.

The government did not charge Guzman with rape. The defense team also accused jurors of "cannily lying" to the judge when he asked them about their exposure to media coverage in Guzman's case.

"We look forward to vindicating his rights in a new trial before a jury that will abide by its oath," defense attorney Eduardo Balarezo said in an email. Guzman faces life in prison at his June sentencing.

After the Vice report was published in February, CBS News legal analyst Rikki Klieman said on CBSN it was possible for Cogan to look past the alleged misconduct. "The jurors may say that the evidence was overwhelming," Klieman said. "There were tapes. There were texts. There were films. There were all kinds of hard pieces of evidence in addition to the 14 cooperating witnesses out of 50-some-odd witnesses during a three-month trial."

If Cogan decides to follow that route, Klieman also said that could set a precedent that jurors could disobey judges without consequences. "I think that is a terrible precedent indeed," she said.