On some elliptic curves with large sha.
Rose, Harvey E. (2000)
Experimental Mathematics
Similarity:
Rose, Harvey E. (2000)
Experimental Mathematics
Similarity:
Clemens Fuchs, Rafael von Känel, Gisbert Wüstholz (2011)
Acta Arithmetica
Similarity:
Rubin, Karl, Silverberg, Alice (2000)
Experimental Mathematics
Similarity:
Cremona, John E., Mazur, Barry (2000)
Experimental Mathematics
Similarity:
Andrej Dujella, Kálmán Győry, Ákos Pintér (2012)
Acta Arithmetica
Similarity:
Gang Yu (2005)
Acta Arithmetica
Similarity:
Ruthi Hortsch (2016)
Acta Arithmetica
Similarity:
We give an asymptotic formula for the number of elliptic curves over ℚ with bounded Faltings height. Silverman (1986) showed that the Faltings height for elliptic curves over number fields can be expressed in terms of modular functions and the minimal discriminant of the elliptic curve. We use this to recast the problem as one of counting lattice points in a particular region in ℝ².
Bartosz Naskręcki (2016)
Banach Center Publications
Similarity:
We discuss the distribution of Mordell-Weil ranks of the family of elliptic curves y² = (x + αf²)(x + βbg²)(x + γh²) where f,g,h are coprime polynomials that parametrize the projective smooth conic a² + b² = c² and α,β,γ are elements from ℚ̅. In our previous papers we discussed certain special cases of this problem and in this article we complete the picture by proving the general results.
Alf Van Der Poorten (1980)
Mémoires de la Société Mathématique de France
Similarity:
Joseph H. Silverman, Armand Brumer (1996)
Manuscripta mathematica
Similarity:
Kevin James, Gang Yu (2006)
Acta Arithmetica
Similarity:
P. G. Walsh (2009)
Acta Arithmetica
Similarity:
R. M. Avanzi, U. M. Zannier (2001)
Acta Arithmetica
Similarity:
Tom Fisher (2015)
Acta Arithmetica
Similarity:
We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over ℚ, i.e. pairs of non-isogenous elliptic curves over ℚ whose 9-torsion subgroups are isomorphic as Galois modules.
Armand Brumer, Oisín McGuinness (1992)
Inventiones mathematicae
Similarity:
Jörn Steuding, Annegret Weng (2005)
Acta Arithmetica
Similarity:
Delaunay, Christophe (2001)
Experimental Mathematics
Similarity: