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Modular curves and 11-rank of quadratic fields. (Courbes modulaires et 11-rang de corps quadratiques.) (French) Zbl 0804.11062

The author exhibits 53 explicit complex quadratic number fields whose ideal class groups admit a subgroup isomorphic to \(\mathbb{Z}/11 \mathbb{Z} \times \mathbb{Z}/11 \mathbb{Z} \times \mathbb{Z}/11 \mathbb{Z}\). The field with the smallest discriminant is \(\mathbb{Q} (\sqrt {-107212102879})\). The author exploits the arithmetic of the modular curves \(X_ 0(23)\) and \(X_ 0(46)\) to obtain his examples.
Reviewer: R.Schoof (Povo)

MSC:

11R29 Class numbers, class groups, discriminants
11R11 Quadratic extensions
11Y40 Algebraic number theory computations

Software:

PARI/GP
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References:

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