On the number of prime divisors of the order of elliptic curves modulo p
Jörn Steuding, Annegret Weng (2005)
Acta Arithmetica
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Jörn Steuding, Annegret Weng (2005)
Acta Arithmetica
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Jörn Steuding, Annegret Weng (2005)
Acta Arithmetica
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Graham Everest, Patrick Ingram, Valéry Mahé, Shaun Stevens (2008)
Acta Arithmetica
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Cremona, John E., Mazur, Barry (2000)
Experimental Mathematics
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Rose, Harvey E. (2000)
Experimental Mathematics
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Touafek, Nouressadat (2008)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Franz Lemmermeyer (2003)
Acta Arithmetica
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J.F. Voloch (1988)
Bulletin de la Société Mathématique de France
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K. Rubin (1987)
Inventiones mathematicae
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Clemens Fuchs, Rafael von Känel, Gisbert Wüstholz (2011)
Acta Arithmetica
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P. G. Walsh (2009)
Acta Arithmetica
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D.L. Ulmer (1990)
Inventiones mathematicae
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Min Sha, Igor E. Shparlinski (2015)
Acta Arithmetica
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We obtain new results concerning the Lang-Trotter conjectures on Frobenius traces and Frobenius fields over single and double parametric families of elliptic curves. We also obtain similar results with respect to the Sato-Tate conjecture. In particular, we improve a result of A. C. Cojocaru and the second author (2008) towards the Lang-Trotter conjecture on average for polynomially parameterised families of elliptic curves when the parameter runs through a set of rational numbers of...
Ruthi Hortsch (2016)
Acta Arithmetica
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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.
Tim Dokchitser (2007)
Acta Arithmetica
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Rubin, Karl, Silverberg, Alice (2000)
Experimental Mathematics
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Joseph H. Silverman (2012)
Acta Arithmetica
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