Rank computations for the congruent number elliptic curves

Experimental Mathematics

Volumn 9, Issue 4, 2000, Pages 591-594

  Rogers, Nicholas F ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034348630     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.2000.10504662     Document Type: Article

References (10)

1. I. Connell, “APECS: Arithmetic of Plane Elliptic Curves”, See ftp.math.mcgill.ca/pub/apecs/. Requires Maple.
2. J. E. Cremona, “mwrank, a program for 2-descent on elliptic curves over ℚ”, last major update 1998. See http://www.maths.nottingham.ac.uk/personal/jec/ftp/progs.
3. F. Gouvea and B. Mazur, “The square-free sieve and the rank of elliptic curves”, J. Amer. Math. Soc. 4: 1 (1991), 1-23.
4. N. Koblitz, Introduction to elliptic curves and modular forms, Graduate Texts in Math. 97, Springer, New York, 1984. Second edition, 1993.
5. G. Kramarz, “All congruent numbers less than 2000”, Math. Ann. 273: 2 (1986), 337-340.
6. F. R. Nemenzo, “All congruent numbers less than 40000”, Proc. Japan Acad. Ser. A Math. Sci. 74: 1 (1998), 29-31.
7. K. Noda and H. Wada, “All congruent numbers less than 10 000”, Proc. Japan Acad. Ser. A Math. Sci. 69: 6 (1993), 175-178.
8. K. Rubin and A. Silverberg, “Ranks of elliptic curves in families of quadratic twists”, Experiment. Math. 9: 4 (2000), 583-590.
9. J. H. Silverman, The arithmetic of elliptic curves, vol. 106, Graduate Texts in Math., Springer, New York, 1986.
10. J. B. Tunnell, “A classical Diophantine problem and modular forms of weight 3/2”, Invent. Math. 72:2 (1983), 323-334.