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ON PAIRINGS IN ELLIPTIC CURVES OVER GLOBAL FIELDS
Mathematics of the USSR-Izvestiya, 1978zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Height estimates for elliptic curves in short Weierstraß form over global fields and a comparison
Archiv der Mathematik, 2001Let \(K\) be a global field and denote by \({\mathcal M}_K\) the set of pairwise inequivalent absolute values \(v\) of \(K\) satisfying the sum formula \(\sum_{v \in {\mathcal M}_K} \lambda_v v(z) = 0\) for all \(z \in K^*\) with multiplicities \(\lambda_v\). Let \(E: Y^2 = X^3 + aX + b\) be an elliptic curve over \(K\).
Zimmer, Horst G., Schmitt, Susanne
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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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Elliptic curves over real quadratic fields are modular
Inventiones Mathematicae, 2014Samir Siksek
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On the torsion of rational elliptic curves over quartic fields
Mathematics of Computation, 2018Enrique Gonzalez-Jimenez +1 more
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Torsion of rational elliptic curves over quartic Galois number fields
Journal of Number Theory, 2016Michael Chou
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Torsion of elliptic curves over cyclic cubic fields
Mathematics of Computation, 2019Maarten Derickx
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