Ms Cooper, who now faces jail, has confessed to misconduct in a judicial or public office by striking up a relationship with a prisoner between August 2014 and July 2015.
Judge Rupert Overbury has adjourned sentencing until October 3 at Ipswich Crown Court.
Ms Cooper had already been sacked from her role at the Category C prison.
Her defence lawyer Andrew Shaw has acknowledged she must face prison as her offence crosses the custody threshold.
Cooper is also alleged to have taken the murderer a Whitney Houston CD and some food Credit: Albanpix The indictment she faces confirms she "sent and disclosed indecent images of herself to the prisoner."
William Carter prosecuting said: "He requested such images and the mere fact he felt able to also tells its own tale.
"Images of the kind requested were found on her phone.
"Whether she sent them or not the Crown will say doesn't really matter that much.
"The fact is she took them and he felt he was able to ask for them".
It was also heard Cooper had taken the murderer a CD and some food.
He added: "The extent of physical or sexual conduct is perhaps relative.
"We are frankly unconcerned whether or not she gave (Dalby) a Whitney Houston CD and the same goes for food.
Cooper struck up the 'inappopriate relationship' with Dalby at HMP Warren Hill in Suffolk Credit: Albanpix Mr Carter continued: "There is another call where the call is conducted as if she is her sister.
"The point being, she was aware the relationship was inappropriate and quite wrong, and sough to conceal it.
In 2009 prison officer Shirley Fowle was said to have been charmed by Dalby.
Colleagues became suspicious when she was caught with two smuggled mobile phones and had money paid into his prison account.
She quit before an investigation into their relationship could be completed.