Supersingular primes for elliptic curves over real number fields
Noam D. Elkies (1989)
Compositio Mathematica
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Noam D. Elkies (1989)
Compositio Mathematica
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René Schoof (1995)
Journal de théorie des nombres de Bordeaux
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We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large ; it is based on Shanks's baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is based on calculations with the torsion points of the elliptic curve [18]. This deterministic...
Philippe Cassou-Noguès, Anupam Srivastav (1990)
Journal de théorie des nombres de Bordeaux
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Everett W. Howe (1993)
Compositio Mathematica
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Masanari Kida (2001)
Journal de théorie des nombres de Bordeaux
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We prove that the -invariant of an elliptic curve defined over an imaginary quadratic number field having good reduction everywhere satisfies certain Diophantine equations under some hypothesis on the arithmetic of the quadratic field. By solving the Diophantine equations explicitly in the rings of quadratic integers, we show the non-existence of such elliptic curve for certain imaginary quadratic fields. This extends the results due to Setzer and Stroeker.
R. J. Stroeker (1979)
Compositio Mathematica
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K. Kramer, J. Tunnell (1982)
Compositio Mathematica
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R. Damerell (1971)
Acta Arithmetica
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