A Remark on the Conjectures of Lang-Trotter and Sato-Tate on Average [PDF]
arXiv, 2007 We obtain new average results on the conjectures of Lang-Trotter and Sato-Tate about elliptic curves.
arxiv
Averages of elliptic curve constants [PDF]
arXiv, 2007 We compute the averages over elliptic curves of the constants occurring in the Lang-Trotter conjecture, the Koblitz conjecture, and the cyclicity conjecture. The results obtained confirm the consistency of these conjectures with the corresponding ``theorems on average'' obtained recently by various authors.
arxiv
Classifying Brumer's quintic polynomials by weak Mordell-Weil groups [PDF]
arXiv, 2008 We develop a general classification theory for Brumer's dihedral quintic polynomials by means of Kummer theory arising from certain elliptic curves. We also give a similar theory for cubic polynomials.
arxiv
An explicit classification for the cyclic rational torsion subgroups of odd order of elliptic curves over $ \Q $ [PDF]
arXiv, 2008 This paper has been withdrawn by the author due to an uninteresting calculation.
arxiv
Rational torsion in elliptic curves and the cuspidal subgroup [PDF]
arXiv, 2008 Let $A$ be an elliptic curve over $\Q$ of square free conductor $N$. We prove that if $A$ has a rational torsion point of prime order $r$ such that $r$ does not divide $6N$, then $r$ divides the order of the cuspidal subgroup of $J_0(N)$.
arxiv
Period and index of genus one curves over number fields [PDF]
arXiv, 2008 The period of a curve is the smallest positive degree of Galois-invariant divisor classes. The index is the smallest positive degree of rational divisors. We construct examples of genus one curves with prescribed period and index over certain number fields.
arxiv
Infinite family of elliptic curves of rank at least 4 [PDF]
arXiv, 2009 We investigate $\mathbb{Q}$-ranks of the elliptic curve $E_t$: $y^2+txy=x^3+tx^2-x+1$ where $t$ is a rational parameter. We prove that for infinitely many values of $t$ the rank of $E_t(\mathbb{Q})$ is at least 4.
arxiv
Selmer Groups of Elliptic Curves with Complex Multiplication [PDF]
Canad. J. Math. vol. 56 (1), 2004 pp. 194--208, 2009 This paper contains some results regarding the Iwasawa module structure of Selmer groups of elliptic curves with complex multiplication.
arxiv
Anti-PD1 'SHR-1210' aberrantly targets pro-angiogenic receptors and this polyspecificity can be ablated by paratope refinement. [PDF]
MAbs, 2019 Finlay WJJ +3 more
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HERON QUADRILATERALS VIA ELLIPTIC CURVES. [PDF]
Rocky Mt J Math, 2017 Izadi F, Khoshnam F, Moody D.
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