Geodesic
On the topology of elliptic curves
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 1, pp. 242-250

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The paper is concerned with studying the everywhere density of the set of rational points on an elliptic curve. V. N. Ushakov's conjecture, which is related to the topology of elliptic curves, is investigated. Elliptic curves and Weierstrass functions with real invariants are considered. A criterion of the everywhere density of a set of points on a curve is proved. The rank of an elliptic curve is calculated numerically.
Keywords: elliptic curve, elliptic integral, everywhere density, rank, $L$-function. 
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N. V. Medvedev; S. S. Titov. On the topology of elliptic curves. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 1, pp. 242-250. http://geodesic.mathdoc.fr/item/TIMM_2012_18_1_a18/