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%I #48 Apr 21 2024 14:29:37
%S 3,5,5,6,11,17,11,17,23,35,35,35,35,35,59,47,65,53,71,71,71,71,89,95,
%T 107,101,107,95,107,107,143,113,119,125,167,143,161,179,179,185,191,
%U 161,167,179,215,179,215,215,209,233,239,215,251,269,239,263,281,287,287,287
%N Number of solutions to the congruence y^2 + x*y + y == x^3 + 4*x - 6 (mod p) as p runs through the primes.
%C This elliptic curve corresponds to a weight 2 newform which is an eta-quotient, namely, eta(t)*eta(2t)*eta(7t)*eta(14t), see Theorem 2 in Martin & Ono.
%H Seiichi Manyama, <a href="/A276173/b276173.txt">Table of n, a(n) for n = 1..1000</a>
%H Yves Martin and Ken Ono, <a href="http://dx.doi.org/10.1090/S0002-9939-97-03928-2">Eta-Quotients and Elliptic Curves</a>, Proc. Amer. Math. Soc. 125, No 11 (1997), 3169-3176.
%F a(n) gives the number of solutions of the congruence y^2 + x*y + y == x^3 + 4*x - 6 (mod prime(n)), n >= 1.
%e The first nonnegative complete residue system {0, 1, ..., prime(n)-1} is used.
%e The solutions (x, y) of y^2 + x*y + y == x^3 + 4*x - 6 (mod prime(n)) begin:
%e n, prime(n), a(n): solutions (x, y)
%e 1, 2, 3: (0, 0), (0, 1), (1, 1)
%e 2, 3, 5: (0, 0), (0, 2), (1, 2),
%e (2, 1), (2, 2)
%e 3, 5, 5: (1, 4), (2, 0), (2, 2),
%e (4, 2), (4, 3)
%e 4, 7, 6: (1, 6), (2, 2), (3, 1),
%e (3, 2), (5, 3), (5, 5)
%Y Cf. A030187, A275742, A276174.
%K nonn,changed
%O 1,1
%A _Seiichi Manyama_, Sep 10 2016
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