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Let $A=E\times E'$ be a surface which is a product of two elliptic curves. Then it is claimed that there is an isomorphism: $$\mathbb Z \oplus {\rm Hom}(E, E')\oplus \mathbb Z \to {\rm NS}(A)$$ defined by $$(a,\lambda,b) \to (a-1)h+\Gamma_\lambda+(b-\deg \lambda)v,$$ where $h, v$ are horizontal and vertical divisors respectively, and $\Gamma_\lambda \subset E \times E'$ is the graph of $\lambda: E \to E'$.

Where is the reference for this result?

I notice the post Neron-Severi group for product of curves on this site and the provided reference, but it gives no clue for such statement.

Thank you!

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    $\begingroup$ This is true (with appropriate modifications) for any product of curves, see Birkenhake-Lange Complex Abelian varieties, Theorem 11.5.1. $\endgroup$
    – abx
    Commented Nov 28, 2019 at 10:54
  • $\begingroup$ Thank you very much! $\endgroup$
    – Li Yutong
    Commented Nov 29, 2019 at 0:28

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