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$2i$ map of an the elliptic curve over $F_p^2$ defined by $y^2=x^3+x$

I am trying to compute the endomorphism $[2i]$ of the elliptic curve map of The elliptic curve over $F_p^2$ defined by $y^2=x^3+x$ such that [2i] o [2i] = [-4]

but I do not know how. the result should be an isogeny

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2i2i map of an the elliptic curve over F2pF_p^2 defined by y2=x3+xy^2=x^3+x

$2i$ map of an the elliptic curve over $F_p^2$ defined by $y^2=x^3+x$