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The local-global principle for divisibility in CM elliptic curves over number fields.
2022We investigate the local-global principle for divisibility by pn in elliptic curves over number fields. For p = 7 we find that the local-global principle for divisibility by pn holds for all n ∈ N for elliptic curves over quadratic fields, but could fail for some elliptic curves over cubic fields. We also extend to the result to certain elliptic curves
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Elliptic Curves over Global Fields and ℓ-Adic Representations
1987In the previous two chapters the local study of elliptic curves was carried out and a substantial part of the theory was related to how the fundamental symmetry, the Frobenius element, behaved on the curve modulo a prime. For an elliptic curve E over a number field K (or more generally any global field), we have for each prime a Frobenius element ...
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An Algorithm for Determining Torsion Growth of Elliptic Curves
Experimental Mathematics, 2023Enrique Gonzalez-Jimenez, Filip Najman
exaly
Global patterns in excess body weight and the associated cancer burden
Ca-A Cancer Journal for Clinicians, 2019Hyuna Sung +2 more
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Elliptic curves over real quadratic fields are modular
Inventiones Mathematicae, 2014Nuno Freitas, Samir Siksek
exaly
Torsion of rational elliptic curves over quartic Galois number fields
Journal of Number Theory, 2016Michael Chou
exaly
Darmon points on elliptic curves over number fields of arbitrary signature
Proceedings of the London Mathematical Society, 2015Xavier Guitart +2 more
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Analyzing the Galbraith-Lin-Scott Point Multiplication Method for Elliptic Curves over Binary Fields
IEEE Transactions on Computers, 2009Koray Karabina, Alfred Menezes
exaly