Geodesic
On ideal class group computation of imaginary multiquadratic fields
Prikladnaâ diskretnaâ matematika, no. 4 (2022), pp. 22-30

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In the paper, we extend Biasse — van Vredendaal (OBS, 2019, vol. 2) implementation and experiments of the class group computation from real to imaginary multiquadratic fields. The implementation is optimized by introducing an explicit prime ideal lift operation and by using LLL reduction instead of HNF computation. We provide examples of class group computation of the imaginary multiquadratic fields of degree 64 and 128, that has been previously unreachable.
Keywords: multiquadratic field, ideal class group. 
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     author = {S. A. Novoselov},
     title = {On ideal class group computation of imaginary multiquadratic fields},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {22--30},
     publisher = {mathdoc},
     number = {4},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PDM_2022_4_a2/}
}
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S. A. Novoselov. On ideal class group computation of imaginary multiquadratic fields. Prikladnaâ diskretnaâ matematika, no. 4 (2022), pp. 22-30. http://geodesic.mathdoc.fr/item/PDM_2022_4_a2/