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2011, Student mathematical library : IAS/Park City mathematical subseries, ISBN 0821852426, Volume 58, xiv, 195
Book
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 05/2018, Volume 87, Issue 311, pp. 1457 - 1478
Let E be an elliptic curve defined over \mathbb{Q} and let G = E(\mathbb{Q})_{\textup {tors}} be the associated torsion subgroup. We study, for a given G,... 
Quartic fields | Rationals | Elliptic curves | Torsion subgroup | MATHEMATICS, APPLIED | QUADRATIC FIELDS | INTEGRAL J-INVARIANT | torsion subgroup | quartic fields | SUBGROUPS | CUBIC NUMBER-FIELDS | BOUNDS | FAMILIES | POINTS | COMPLEX MULTIPLICATION | rationals
Journal Article
Mathematical Research Letters, ISSN 1073-2780, 2017, Volume 24, Issue 4, pp. 1067 - 1096
In this article, we study the minimal degree [K(T) : K] of a p-subgroup T subset of E((K) over bar)(tors) for an elliptic curve E/K defined over a number field... 
MATHEMATICS | POINTS | QUADRATIC FIELDS
Journal Article
Mathematische Annalen, ISSN 0025-5831, 9/2013, Volume 357, Issue 1, pp. 279 - 305
... over the rationals Álvaro Lozano-Robledo Received: 18 December 2011 / Revised: 16 December 2012 / Published online: 2 February 2013 © Springer-Verlag Berlin Heidelberg 2013... 
Mathematics, general | Mathematics | MATHEMATICS | GALOIS PROPERTIES | ORDER | BOUNDS | ISOGENY | NUMBER-FIELDS
Journal Article
Journal of Number Theory, ISSN 0022-314X, 2010, Volume 130, Issue 3, pp. 539 - 558
Let K be a quadratic imaginary number field with discriminant D K ≠ − 3 , − 4 and class number one. Fix a prime p ⩾ 7 which is unramified in K. Given an... 
Bernoulli–Hurwitz numbers | Elliptic curves | Wieferich places | p-Adic Galois representations | Elliptic units | Complex multiplication | Bernoulli-Hurwitz numbers | ELLIPTIC-CURVES | SURJECTIVITY | IWASAWA THEORY | IMAGINARY QUADRATIC FIELDS | MATHEMATICS | KUMMER | CRITERION | UNITS | Statistics | Questions and answers
Journal Article
manuscripta mathematica, ISSN 0025-2611, 7/2008, Volume 126, Issue 3, pp. 393 - 407
...manuscripta math. 126, 393–407 (2008) © Springer-Verlag 2008 Álvaro Lozano-Robledo Ranks of abelian varieties over infinite extensions of the rationals Received... 
Geometry | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Primary 11G05 | 14K15 | Algebraic Geometry | Mathematics, general | Mathematics | Number Theory | ROOT NUMBERS | MATHEMATICS | ELLIPTIC-CURVES | FIELDS | PARITY | DIVISION TOWERS | VALUES | Calderas
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2018, Volume 87, Issue 309, pp. 425 - 458
Let E/\mathbb{Q} be an elliptic curve and let \mathbb{Q}(3^\infty ) be the compositum of all cubic extensions of \mathbb{Q}. In this article we show that the... 
ELEMENTARY ABELIAN 2-EXTENSIONS | MATHEMATICS, APPLIED | MODULAR-CURVES | BOUNDS | ISOGENIES | FAMILIES | VARIETIES | POINTS | NUMBER-FIELDS | Mathematics - Number Theory
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 8/2016, Volume 283, Issue 3, pp. 835 - 859
... · Álvaro Lozano-Robledo 2 Received: 22 April 2015 / Accepted: 18 December 2015 / Published online: 8 February 2016 © Springer-Verlag Berlin Heidelberg 2016 Abstract... 
Secondary 14H52 | Elliptic curves | Abelian number fields | Primary 11G05 | Mathematics, general | Torsion points | Mathematics | Division fields | MATHEMATICS | GALOIS PROPERTIES | REPRESENTATIONS | FINITE-ORDER | 2-EXTENSIONS | SURJECTIVITY
Journal Article
Journal of number theory, ISSN 0022-314X, 06/2020
Journal Article
Research in number theory, ISSN 2363-9555, 2018, Volume 4, Issue 1, pp. 1 - 39
...Lozano-Robledo Res. Number Theory (2018) 4:6 https://doi.org/10.1007/s40993-018-0095-0 RESEARCH Uniform boundedness in terms of ramification Álvaro Lozano... 
Secondary 14H52 | Mathematics | Number Theory | Primary 11G05
Journal Article
Journal of number theory, ISSN 0022-314X, 10/2020, Volume 215, pp. 339 - 361
Let X:y2=f(x) be a hyperelliptic curve over Q(T) of genus g≥1. Assume that the jacobian of X over Q(T) has no subvariety defined over Q. Denote by Xt the... 
Hyper-elliptic curves | Rank | Bias | Jacobians
Journal Article
Journal of Number Theory, ISSN 0022-314X, 2006, Volume 117, Issue 2, pp. 439 - 470
Let K be a quadratic imaginary number field with discriminant D K ≠ - 3 ,- 4 and class number one. Fix a prime p ⩾ 7 which is not ramified in K and write h p... 
Elliptic units | Elliptic curves | p-adic Galois representations | P-adic Galois representations | MATHEMATICS | SURJECTIVITY | CRITERION | elliptic curves | elliptic units | IMAGINARY QUADRATIC FIELDS
Journal Article
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