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

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