AbstractWe show that the number of elliptic curves over Q with conductor N is ⪡εN1/4+ε, and for almost all positive integers N, this can be improved to ⪡εNε. The second estimate follows from a theorem of Davenpart and Heilbronn on the average size of the 3-class groups of quadratic fields. The first estimate follows from the fact that the 3-class group of a quadratic field Q(D) has size ⪡ε|D|1/4+ε, a non-trivial improvement over the Brauer–Siegel estimate
In joint work with Manjul Bhargava (see [7]), we proved that the average rank of rational elliptic c...
In this paper is considered the average size of the 2‐Selmer groups of a class of quadratic twists o...
Given an elliptic curve E and a positive integer N, we consider the problem of counting the number o...
AbstractWe show that the number of elliptic curves over Q with conductor N is ⪡εN1/4+ε, and for almo...
It is proved that the 3-part of the class number of a quadratic field Q( D) is O(|D|55/112+) in gene...
We give new bounds for the number of integral points on elliptic curves. The method may be said to i...
[[abstract]]Let D be an integer. Consider the elliptic curve E/Q :y2 = x3 + D, which has j-invariant...
AbstractLet E be an elliptic curve over Q of conductor N and K be an imaginary quadratic field, wher...
Let E be an elliptic curve defined over Fq, the finite field of q elements. We show that for some co...
We present a lower bound for the exponent of the group of rational points of an elliptic curve over ...
We present a lower bound for the exponent of the group of rational points of an elliptic curve over ...
Let K be a number field and E/K be an elliptic curve with no 2‑torsion points. In the present articl...
In this thesis, we prove that the average rank of j-invariant 0 elliptic curves, when ordered by dis...
AbstractLet K be a number field and Ei/K an elliptic curve defined over K for i=1,2,3,4. We prove th...
AbstractWe explain how recent work on 3-descent and 4-descent for elliptic curves over Q can be comb...
In joint work with Manjul Bhargava (see [7]), we proved that the average rank of rational elliptic c...
In this paper is considered the average size of the 2‐Selmer groups of a class of quadratic twists o...
Given an elliptic curve E and a positive integer N, we consider the problem of counting the number o...
AbstractWe show that the number of elliptic curves over Q with conductor N is ⪡εN1/4+ε, and for almo...
It is proved that the 3-part of the class number of a quadratic field Q( D) is O(|D|55/112+) in gene...
We give new bounds for the number of integral points on elliptic curves. The method may be said to i...
[[abstract]]Let D be an integer. Consider the elliptic curve E/Q :y2 = x3 + D, which has j-invariant...
AbstractLet E be an elliptic curve over Q of conductor N and K be an imaginary quadratic field, wher...
Let E be an elliptic curve defined over Fq, the finite field of q elements. We show that for some co...
We present a lower bound for the exponent of the group of rational points of an elliptic curve over ...
We present a lower bound for the exponent of the group of rational points of an elliptic curve over ...
Let K be a number field and E/K be an elliptic curve with no 2‑torsion points. In the present articl...
In this thesis, we prove that the average rank of j-invariant 0 elliptic curves, when ordered by dis...
AbstractLet K be a number field and Ei/K an elliptic curve defined over K for i=1,2,3,4. We prove th...
AbstractWe explain how recent work on 3-descent and 4-descent for elliptic curves over Q can be comb...
In joint work with Manjul Bhargava (see [7]), we proved that the average rank of rational elliptic c...
In this paper is considered the average size of the 2‐Selmer groups of a class of quadratic twists o...
Given an elliptic curve E and a positive integer N, we consider the problem of counting the number o...
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