An Australian court has been told that the crimes of mushroom murderer Erin Patterson were "truly dreadful" and that she should never be allowed to leave prison.

Crown prosecutors are appealing against a sentence they call "manifestly inadequate" as it allows for the possibility of parole.

Patterson was jailed for life after killing three of her relatives and trying to kill another by serving them a beef Wellington containing death cap mushrooms at her Victoria home in 2023.

The 51-year-old, who attended the Court of Appeal via video link from prison, will be eligible to be freed after 33 years.

The Court of Appeal in Melbourne has also heard a challenge from Patterson's lawyers as they try to overturn her convictions.

The judges say they will reserve their decisions, meaning it will likely be weeks or months before the outcome of both appeals is known.

Patterson's victims include her in-laws Don and Gail Patterson, both 70, and Gail's sister Heather Wilkinson, 66, who all died after what prosecutors called "shocking illnesses" as a result of the poisoning.

The only surviving guest, Heather's husband Ian Wilkinson, has never fully recovered from his ordeal, they said.