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A006962
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Supersingular primes of the elliptic curve X_0 (11).
(Formerly M2115)
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2
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2, 19, 29, 199, 569, 809, 1289, 1439, 2539, 3319, 3559, 3919, 5519, 9419, 9539, 9929, 11279, 11549, 13229, 14489, 17239, 18149, 18959, 19319, 22279, 24359, 27529, 28789, 32999, 33029, 36559, 42899, 45259, 46219, 49529, 51169, 52999, 55259
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OFFSET
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1,1
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COMMENTS
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The primes for which A006571(p) == 0 (mod p) are called supersingular for the elliptic curve "11a3" and form sequence A006962. A prime p>2 is in A006962 if and only if A006571(p) = 0. - Michael Somos, Dec 25 2010
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MATHEMATICA
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maxPi = 500; QP = QPochhammer; s = q*(QP[q]*QP[q^11])^2 + O[q]^(Prime[ maxPi] + 1); Reap[Do[If[Mod[SeriesCoefficient[s, p], p] == 0, Print[p]; Sow[p]], {p, Prime[Range[maxPi]]}]][[2, 1]] (* Jean-François Alcover, Nov 29 2015, adapted from PARI *)
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PROG
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(PARI) forprime(p=2, 2999, if(polcoeff(x * sqr(eta(x + O(x^p)) * eta(x^11 + O(x^p))), p)%p == 0, print1(p", "))) /* Michael Somos, Dec 25 2010 */
{ N = 10^8 + 2;
default(seriesprecision, N);
V = Vec((eta(q) * eta(q^11))^2);
forprime(p=2, N, if( V[p]%p == 0, print1(p, ", ") ) );
(Ruby)
require 'prime'
ary = []
cnt = 1
Prime.each(10 ** 7){|p|
a = Array.new(p, 0)
(0..p - 1).each{|i| a[(i * i) % p] += 1}
s = 0
(0..p - 1).each{|i|
s += a[(i * i * i - 4 * i * i + 16) % p]
break if s > p
}
if p == s
ary << p
cnt += 1
return ary if cnt > n
end
}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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