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A006962 Supersingular primes of the elliptic curve X_0 (11).
(Formerly M2115)
2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Joerg Arndt, Table of n, a(n) for n = 1..747 (first 60 terms by Seiichi Manyama)

S. Lang and H. F. Trotter, Frobenius Distribution in GL_2-Extensions Lect Notes Math. 504, 1976, see p. 267.

MATHEMATICA

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-Fran├žois Alcover, Nov 29 2015, adapted from PARI *)

PROG

(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 */

(PARI) \\ gp -s 30G < A006962.gp

{ 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, ", ") ) );

} \\ Joerg Arndt, Sep 10 2016

(Ruby)

require 'prime'

def A006962(n)

  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

  }

end # Seiichi Manyama, Sep 10 2016

CROSSREFS

Cf. A006571.

Sequence in context: A083689 A102617 A120276 * A261312 A090819 A254897

Adjacent sequences:  A006959 A006960 A006961 * A006963 A006964 A006965

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(29)-a(38) from from Michael Somos, Dec 25 2010

STATUS

approved

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Last modified September 25 16:57 EDT 2016. Contains 276540 sequences.