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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

Table of n, a(n) for n=1..38.

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 */

CROSSREFS

Cf. A006571.

Sequence in context: A083689 A102617 A120276 * A261312 A090819 A254897

Adjacent sequences:  A006959 A006960 A006961 * A006963 A006964 A006965

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Michael Somos, Dec 25 2010

STATUS

approved

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Last modified May 24 13:47 EDT 2016. Contains 273241 sequences.