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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 from 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-François 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: A290163 A284496 A120276 * A261312 A090819 A254897
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(29)-a(38) from Michael Somos, Dec 25 2010
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)