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Original Articles

Rank Computations for the Congruent Number Elliptic Curves

Pages 591-594 | Published online: 04 Apr 2012

REFERENCES

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

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