On the equation

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

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

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

MathSciNet review:
726003

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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 and H. P. F. Swinnerton-Dyer,*Notes on elliptic curves. II*, J. Reine Angew. Math.**218**(1965), 79–108. MR**0179168****[2]**J. W. S. Cassels,*Diophantine equations with special reference to elliptic curves*, J. London Math. Soc.**41**(1966), 193–291. MR**0199150****[3]**L. J. Mordell,*The diophantine equation 𝑥⁴+𝑚𝑦⁴=𝑧².*, Quart. J. Math. Oxford Ser. (2)**18**(1967), 1–6. MR**0210659****[4]**L. J. Mordell,*The diophantine equation 𝑦²=𝐷𝑥⁴+1*, Number Theory (Colloq., János Bolyai Math. Soc., Debrecen, 1968), North-Holland, Amsterdam, 1970, pp. 141–145. MR**0272711****[5]**Ernst S. Selmer,*A conjecture concerning rational points on cubic curves*, Math. Scand.**2**(1954), 49–54. MR**0062767**

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

Article copyright:
© Copyright 1984
American Mathematical Society