Let C be an algebraic curve embedded transversally in a power E-N of an elliptic curve E with complex multiplication. We produce a good explicit bound for the height of all the algebraic points on C contained in the union of all proper algebraic subgroups of E-N. The method gives a totally explicit version of the Manin-Demjanenko theorem in the elliptic case and complements previous results only proved when E does not have complex multiplication.
EXPLICIT HEIGHT BOUNDS FOR K-RATIONAL POINTS ON TRANSVERSE CURVES IN POWERS OF ELLIPTIC CURVES
Veneziano, F;
2021-01-01
Abstract
Let C be an algebraic curve embedded transversally in a power E-N of an elliptic curve E with complex multiplication. We produce a good explicit bound for the height of all the algebraic points on C contained in the union of all proper algebraic subgroups of E-N. The method gives a totally explicit version of the Manin-Demjanenko theorem in the elliptic case and complements previous results only proved when E does not have complex multiplication.
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