Arithmetically exceptional lattès maps attached to elliptic curves without complex multiplication

Date

2023-6-20

Author

Odabaş, Oğuzhan

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Let E be an elliptic curve given by y2 = x3 + Ax + B. If E has complex multiplication, then under certain conditions, there is a formula to compute the value sets of Lattès maps induced by such curves. However, when the endomorphism ring of E consists only of the integers, then there is no known method to compute the value sets of Lattès maps attached to such curves. In this thesis, we will introduce a Pari/GP code that computes the value sets of Lattès maps attached to elliptic curves without complex multiplication and discuss the arithmetic exceptionality of these maps experimentally.

Subject Keywords

Elliptic curve, Lattès map, Arithmetically exceptional maps

URI

https://hdl.handle.net/11511/104466

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Graduate School of Natural and Applied Sciences, Thesis