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How can i know if a field is monigenic?

I know the next field is monogenic but sagameth doesn't give me a power basis.

c=sqrt(-(5+2*sqrt(5))) L.<c>=QQ[c] OL=L.maximal_order() B=OL.basis() L;OL;B;L.integral_basis()

Number Field in a with defining polynomial x^4 + 10x^2 + 5 with a = 0.?e-18 + 3.077683537175254?I Maximal Order in Number Field in a with defining polynomial x^4 + 10x^2 + 5 with a = 0.?e-18 + 3.077683537175254?I [3/8a^3 + 3/8a^2 + 1/8a + 1/8, 3/4a^3 + 1/4a, 1/2a^3 + 1/2a^2, a^3] [3/8a^3 + 3/8a^2 + 1/8a + 1/8, 3/4a^3 + 1/4a, 1/2a^3 + 1/2a^2, a^3]

How can i know if a field is monigenic?

I know the next field is monogenic but ~~sagameth~~ SageMath doesn't give me a power basis.

c=sqrt(-(5+2*sqrt(5))) L.<c>=QQ[c] OL=L.maximal_order() B=OL.basis() L;OL;B;L.integral_basis()

sage: c = sqrt(-(5+2*sqrt(5))) sage: L.<c> = QQ[c] sage: OL = L.maximal_order() sage: B = OL.basis() sage: L Number Field in a with defining polynomial x^4 + 10x^2 10*x^2 + 5 with a = 0.?e-18 + 3.077683537175254?I 3.077683537175254?*I sage: OL Maximal Order in Number Field in a with defining polynomial x^4 + 10x^2 10*x^2 + 5 with a = 0.?e-18 + 3.077683537175254?I [3/8a^3 3.077683537175254?*I sage: B [3/8*a^3 + 3/8a^2 3/8*a^2 + 1/8a 1/8*a + 1/8, 3/4a^3 3/4*a^3 + 1/4a, 1/2a^3 1/4*a, 1/2*a^3 + 1/2a^2, 1/2*a^2, a^3] [3/8a^3 sage: L.integral_basis() [3/8*a^3 + 3/8a^2 3/8*a^2 + 1/8a 1/8*a + 1/8, 3/4a^3 3/4*a^3 + 1/4a, 1/2a^3 1/4*a, 1/2*a^3 + 1/2a^2, a^3] 1/2*a^2, a^3]