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A006962 Supersingular primes of the elliptic curve X_0 (11).

%I A006962 M2115 #50 Jan 16 2018 02:37:32
%S A006962 2,19,29,199,569,809,1289,1439,2539,3319,3559,3919,5519,9419,9539,
%T A006962 9929,11279,11549,13229,14489,17239,18149,18959,19319,22279,24359,
%U A006962 27529,28789,32999,33029,36559,42899,45259,46219,49529,51169,52999,55259
%N A006962 Supersingular primes of the elliptic curve X_0 (11).
%C A006962 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
%D A006962 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006962 Joerg Arndt, <a href="/A006962/b006962.txt">Table of n, a(n) for n = 1..747</a> (first 60 terms from Seiichi Manyama)
%H A006962 S. Lang and H. F. Trotter, <a href="http://dx.doi.org/10.1007/BFb0082087">Frobenius Distribution in GL_2-Extensions</a> Lect Notes Math. 504, 1976, see p. 267.
%t A006962 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 *)
%o A006962 (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 */
%o A006962 (PARI) \\ gp -s 30G < A006962.gp
%o A006962 { N = 10^8 + 2;
%o A006962 default(seriesprecision,N);
%o A006962 V = Vec((eta(q) * eta(q^11))^2);
%o A006962 forprime(p=2,N, if( V[p]%p == 0, print1(p,", ") ) );
%o A006962 } \\ _Joerg Arndt_, Sep 10 2016
%o A006962 (Ruby)
%o A006962 require 'prime'
%o A006962 def A006962(n)
%o A006962   ary = []
%o A006962   cnt = 1
%o A006962   Prime.each(10 ** 7){|p|
%o A006962     a = Array.new(p, 0)
%o A006962     (0..p - 1).each{|i| a[(i * i) % p] += 1}
%o A006962     s = 0
%o A006962     (0..p - 1).each{|i|
%o A006962       s += a[(i * i * i - 4 * i * i + 16) % p]
%o A006962       break if s > p
%o A006962     }
%o A006962     if p == s
%o A006962       ary << p
%o A006962       cnt += 1
%o A006962       return ary if cnt > n
%o A006962     end
%o A006962   }
%o A006962 end # _Seiichi Manyama_, Sep 10 2016
%Y A006962 Cf. A006571.
%K A006962 nonn
%O A006962 1,1
%A A006962 _N. J. A. Sloane_
%E A006962 a(29)-a(38) from _Michael Somos_, Dec 25 2010