Improvements in the computation of ideal class groups of imaginary quadratic number fields

Jean-François Biasse

doi:10.3934/amc.2010.4.141

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2010, Volume 4, Issue 2: 141-154. Doi: 10.3934/amc.2010.4.141

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Improvements in the computation of ideal class groups of imaginary quadratic number fields

Jean-François Biasse^1,

1.
LIX - École Polytechnique, 91128 Palaiseau

Received: April 30, 2009

Revised: January 31, 2010

Published: April 2010

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Abstract

We investigate improvements to the algorithm for the computation of ideal class groups described by Jacobson in the imaginary quadratic case. These improvements rely on the large prime strategy and a new method for performing the linear algebra phase. We achieve a significant speed-up and are able to compute ideal class groups with discriminants of 110 decimal digits in less than a week.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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