How to calculate the product of the below multiplication of prime ideals in Z[√(-5)]?
(2, 1-√(-5))(3, 1+√(-5))
I know it can be firstly expressed as a non-principal ideal generated by three numbers in Z[√(-5)],
(6, 2+2√(-5), 3-3√(-5))
but I don't know if it can be further simplified (and how, if it can).
Thanks for your help!