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Positive integers k satisfying y^2 = x^5 - k where x^5 and y^2 are not both divisible by 2^10 and k = 2^(2*m)*d with d a positive squarefree integer d = 7 (mod 8) such that the class number of Q(sqrt(-d)) is not divisible by 5.
3

%I #11 Feb 01 2021 22:12:04

%S 1,16,19,32,32,341,608,768,2816

%N Positive integers k satisfying y^2 = x^5 - k where x^5 and y^2 are not both divisible by 2^10 and k = 2^(2*m)*d with d a positive squarefree integer d = 7 (mod 8) such that the class number of Q(sqrt(-d)) is not divisible by 5.

%D Michael Stoll, On the arithmetic of curves y^2=x^l+A and their Jacobians, J. Reine Angew. Math. 501 (1998), 171-189, see p. 179.

%Y Cf. A034011, A034013, A034014.

%K nonn,fini,full

%O 1,2

%A _N. J. A. Sloane_

%E Title improved by _Sean A. Irvine_, Jul 29 2020