Computing Hilbert Class Polynomials.

Keywords

Chinese remainder theorem, Class (philosophy), Discriminant, Polynomial, Remainder

References

• A course in computational algebraic number theoryHenri Cohen — 1993
• Abelian varieties over finite fieldsWilliam C. Waterhouse — 1969
• Modern computer algebraJ. Gathen, Jürgen Gerhard — 2002
• CONSTRUCTING ELLIPTIC CURVES WITH A KNOWN NUMBER OF POINTS OVER A PRIME FIELDAmod Agashé, Kristin Lauter, Ramarathnam Venkatesan — 2001
• ELLIPTIC CURVES AND PRIMALITY PROVINGA. O. L. Atkin, François Morain — 1993
• On the Class-Number of the Corpus P(√−k)J. E. Littlewood — 1928
• Constructing elliptic curves over finite fields using double eta-quotientsAndreas Enge, Reinhard Schertz — 2004
• The complexity of class polynomial computation via floating point approximationsAndreas Enge — 2006
• Weber's class invariants revisitedReinhard Schertz — 2002
• Counting points on elliptic curves over finite fieldsRené Schoof — 1995
• A p-adic algorithm to compute the Hilbert class polynomialReinier Bröker — 2008
• Die Typen der Multiplikatorenringe elliptischer FunktionenkörperMax Deuring — 1941
• Hilbert’s 12th Problem, Complex Multiplication and Shimura ReciprocityPeter Stevenhagen — 2001
• Einige Bemerkungen zu der vorstehenden Arbeit des Herrn G. Pólya: Über die Verteilung der quadratischen Reste und NichtresteJoan Brodsky Schur — 1918

Cited by

• A course in computational algebraic number theoryHenri Cohen — 1993
• Some remarks on the construction of class polynomialsElisavet Konstantinou, Aristides Kontogeorgis — 2011
• Accelerating the CM methodAndrew V. Sutherland — 2010
• Explicit computations in Iwasawa theoryReinier Bröker, David Hubbard, Lawrence C. Washington — 2018
• Isogeny volcanoesAndrew V. Sutherland — 2012

Related papers

• Computing Hilbert Class PolynomialsJuliana Belding, Reinier Bröker, Andreas Enge — 2008
• Algorithmic Number Theory: First International Symposium, ANTS-I, Ithaca, NY, USA, May 6 - 9, 1994. ProceedingsLeonard M. Adleman, Ming-Deh A. Huang — 1994
• Constructing elliptic curves with a given number of points over a finite fieldAmod Agashé, Kristin Lauter, Ramarathnam Venkatesan — 2001
• Computing Igusa class polynomialsMarco Streng — 2009
• Algorithms for exact polynomial root calculationLee E. Heindel — 1970
• Linear complexity for sequences with characteristic polynomial ƒvAlex J. Burrage, Ana Sălăgean, Raphaël C.‐W. Phan — 2011