The order of the elliptic fiber E_t in Kum(E1×E2) is exactly d(n)=n (odd n) or n/2 (even n), with one subtle CM exception, and every integer occurs as some order.
Torsion dans le groupe de Chow de codimension deux
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Elliptic constant cycle curves on Kummer surfaces
The order of the elliptic fiber E_t in Kum(E1×E2) is exactly d(n)=n (odd n) or n/2 (even n), with one subtle CM exception, and every integer occurs as some order.