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Given a CM field we can use its maximal order (and a choice of CM type) to construct an abelian variety $\mathbb{C}^g/\Lambda$ with complex multiplication by the maximal order.

How do I (or where can I find information on) explicitly write down equations for a projective embedding of this variety, and the action of the CM order on points? Is this implemented anywhere?

For genus one we can use the Eisenstein series to find the coefficients of a Weierstrass model for the elliptic curve. So I'm looking for a generalization of this.
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Given a CM field we can use its maximal order (and a choice of CM type) to construct an abelian variety $\mathbb{C}^g/\Lambda$.\mathbb{C}^g/\Lambda$ with complex multiplication by the maximal order.

How do I (or where can I find information on) explicitly write down equations for a projective embedding of this variety? Is this implemented anywhere?

For genus one we can use the Eisenstein series to find the coefficients of a Weierstrass model for the elliptic curve. So I'm looking for a generalization of this.
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CM field to Torus to Abelian Variety?

Given a CM field we can use its maximal order (and a choice of CM type) to construct an abelian variety $\mathbb{C}^g/\Lambda$.

How do I (or where can I find information on) explicitly write down equations for a projective embedding of this variety? Is this implemented anywhere?

For genus one we can use the Eisenstein series to find the coefficients of a Weierstrass model for the elliptic curve. So I'm looking for a generalization of this.