

A274351


a(n) is the first term of the nth proper elliptic 6cycle.


0



274723, 13415557, 27103147, 127827253, 154689319, 162097909, 183192157, 196484569, 196484569, 246836983, 246948451, 279990229, 281840539, 338131501, 351159649, 392743807, 428156821, 435821443, 459898531
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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_{n1}; 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 6cycle 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 6cycles is based on work done by J. Bahr, Y. Kim, E. Neyman, and G. Taylor.


REFERENCES

L. C. Washington, Number Theory: Elliptic Curves and Cryptography, Chapman & Hall/CRC, 2nd ed., (2008).


LINKS

Table of n, a(n) for n=1..19.
L. Babinkostova et al., Elliptic Reciprocity, arXiv:1212.1983 [math.NT], 2012.
R. Broker and P. Stevenhagen, Constructing elliptic curves of prime order, Contemporary Mathematics 463 (2008), 1728.
R. Broker and P. Stevenhagen, Constructing elliptic curves of prime order, arXiv:0712.2022 [math.NT], 2007.
J. H. Silverman and K. E. Stange, Amicable pairs and aliquot cycles for elliptic curves, arXiv:0912.1831 [math.NT], 2009.
J. H. Silverman and K. E. Stange, Amicable pairs and aliquot cycles for elliptic curves, Experimental Mathematics , 20:3 (2011), 329357.


CROSSREFS

Sequence in context: A256364 A250509 A164520 * A114664 A069372 A157839
Adjacent sequences: A274348 A274349 A274350 * A274352 A274353 A274354


KEYWORD

nonn


AUTHOR

Liljana Babinkostova, Jun 18 2016


STATUS

approved



