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A274351
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a(n) is the first term of the n-th proper elliptic 6-cycle.
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0
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274723, 13415557, 27103147, 127827253, 154689319, 162097909, 183192157, 196484569, 196484569, 246836983, 246948451, 279990229, 281840539, 338131501, 351159649, 392743807, 428156821, 435821443, 459898531
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OFFSET
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1,1
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COMMENTS
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An elliptic pair over a squarefree integer d is a pair of primes (p,q) such that there exists an elliptic curve E with complex multiplication in the imaginary quadratic field with d<0 which has order q when examined over a prime field of size p.
The symbol (p_1, p_2, ..., p_n)_d denotes an elliptic list of length n over d if each of (p_1,p_2), (p_2, p_3), ..., (p_{n-1}; p_n) is an elliptic pair over d. An elliptic cycle is an elliptic list with p_n = p_1. A proper elliptic cycle is one where this is the only equality among terms. The formula for the rest of the terms in a (proper) elliptic 6-cycle is given in Corollary 3.2.in the paper arXiv:1212.1983. Also, some of the results about elliptic pairs and cycles appear in arXiv:1212.1983. The resulting sequence of 6-cycles is based on work done by J. Bahr, Y. Kim, E. Neyman, and G. Taylor.
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REFERENCES
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L. C. Washington, Number Theory: Elliptic Curves and Cryptography, Chapman & Hall/CRC, 2nd ed., (2008).
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LINKS
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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