Idaho prosecutors may have evidence that indicates Lori Vallow participated in the killing of her two children, Tylee Ryan and Joshua "JJ" Vallow.

Earlier this month, Lori Vallow's attorneys filed a motion asking the judge to declare the death penalty unconstitutional. In the document, her legal team also claimed prosecutors have not shared enough details as to why their client is eligible for the death penalty.

On Thursday, prosecutors filed an objection, claiming evidence would prove Vallow qualifies for the death penalty.

"Sufficient evidence existed for the grand jury to find probable cause that the defendant intended for her children and Tammy Daybell to die," Fremont County Prosecuting Attorney Lindsey Blake wrote in the response.

"Further, there is sufficient evidence for a jury to conclude that the defendant participated in the killing of her own children."

The motion comes after Vallow's team filed a notice informing the court of her alibi at the time of her children's deaths and the death of her husband Chad Daybell's late wife, Tammy Daybell.

"The evidence the state will introduce at trial, some of which have already been reviewed by the Grand Jury, will show that the defendant intended for her children and her boyfriend's wife to die and that she affirmatively acted to make those deaths happen," Blake said.

In a notice of alibi, Lori Vallow's attorneys claimed Tylee and JJ died at her brother Alex Cox's apartment while she was in her own apartment. Vallow's legal team also claimed she was in Hawaii when Tammy Daybell died.

Lori Vallow and Chad Daybell have pleaded not guilty to several counts of first-degree murder and conspiracy to commit murder. Their trial is scheduled to begin on April 3 in Ada County, Idaho.

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Police are investigating a shooting incident at the Oakland Tech High School. In this representational image, a police tape hangs across North Camden Street in Minneapolis, Minnesota, June 24, 2018. Stephen Maturen/Getty Images