How to multiply these two prime ideals in Z[√(-5)]?

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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!