22 citations · 80 across the 8 of their papers we have counts for
10 papers
Elliptic curve rank growth in multi-quadratic extensions
Dylan T. Costa, Álvaro Lozano-Robledo
In this article we give an algorithm to produce infinitely many explicit quadratic twists of a given elliptic curve over with a rational point and fixed root number. M…
Models of CM elliptic curves with a prescribed -adic Galois image
Enrique González-Jiménez, Álvaro Lozano-Robledo, Benjamin York
For each prime number and for each imaginary quadratic order of class number one or two, we determine all the possible -adic Galois representations that occur for any…
Elliptic curves with complex multiplication and abelian division fields
Asimina S. Hamakiotes, Alvaro Lozano-Robledo
Let be an imaginary quadratic field, and let be an order in of conductor . Let be an elliptic curve with CM by , such th…
Rank and Bias in Families of Hyperelliptic Curves via Nagao's Conjecture
Trajan Hammonds, Seoyoung Kim, Benjamin Logsdon +2
Let be a hyperelliptic curve over of genus . Assume that the jacobian of over has no subvariety de…
A probabilistic model for the distribution of ranks of elliptic curves over
Alvaro Lozano-Robledo
In this article, we propose a new probabilistic model for the distribution of ranks of elliptic curves in families of fixed Selmer rank, and compare the predictions with previous r…
On the torsion of rational elliptic curves over quartic fields
Enrique Gonzalez-Jimenez, Alvaro Lozano-Robledo
Let E be an elliptic curve defined over Q and let G = E(Q)_tors be the associated torsion subgroup. We study, for a given G, which possible groups G <= H could appear such that H=E…
On the minimal degree of definition of p-primary torsion subgroups of elliptic curves
Enrique Gonzalez-Jimenez, Alvaro Lozano-Robledo
In this article, we study the minimal degree [K(T):K] of a p-subgroup T <= E(\overline{K})_tors for an elliptic curve E/K defined over a number field K. Our results depend on the s…
Elliptic Curves with abelian division fields
Enrique Gonzalez-Jimenez, Alvaro Lozano-Robledo
Let E be an elliptic curve over Q, and let n=>1. The central object of study of this article is the division field Q(E[n]) that results by adjoining to Q the coordinates of all n-t…
Torsion subgroups of rational elliptic curves over the compositum of all cubic fields
Harris B. Daniels, Alvaro Lozano-Robledo, Filip Najman +1
Let be an elliptic curve and let be the compositum of all cubic extensions of . In this article we show that the torsion subgroup…
Constructing Elliptic Curves over with Moderate Rank
Scott Arms, Steven J. Miller, Alvaro Lozano-Robledo
We give several new constructions for moderate rank elliptic curves over . In particular we construct infinitely many rational elliptic surfaces (not in Weierstrass…