On the equation

Authors:
A. Bremner and J. W. S. Cassels

Journal:
Math. Comp. **42** (1984), 257-264

MSC:
Primary 11D25; Secondary 11G05, 14G05

DOI:
https://doi.org/10.1090/S0025-5718-1984-0726003-4

MathSciNet review:
726003

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Abstract | References | Similar Articles | Additional Information

Abstract: Generators are found for the group of rational points on the title curve for all primes less than 1,000. The rank is always 1 in accordance with conjectures of Selmer and Mordell. Some of the generators are rather large.

**[1]**B. J. Birch & H. P. F. Swinnerton-Dyer, "Notes on elliptic curves II,"*J. Reine Angew. Math.*, v. 218, 1965, pp. 79-108. MR**0179168 (31:3419)****[2]**J. W. S. Cassels, "Diophantine equations with special reference to elliptic curves,"*J. London Math. Soc.*, v. 41, 1966, pp. 193-291. MR**0199150 (33:7299)****[3]**L. J. Mordell, "The diophantine equation ,"*Quart. J. Math.*(2), v. 18, 1967, pp. 1-6. MR**0210659 (35:1545)****[4]**L. J. Mordell, , Number Theory Colloquium, János Bolyai Math. Soc., Debrecen, 1968, pp. 141-145 (North-Holland, Amsterdam, 1970). MR**0272711 (42:7592)****[5]**E. Selmer, "A conjecture concerning rational points on cubic curves,"*Math. Scand.*, v. 2, 1954, pp. 49-54. MR**0062767 (16:14g)**

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DOI:
https://doi.org/10.1090/S0025-5718-1984-0726003-4

Article copyright:
© Copyright 1984
American Mathematical Society