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It appears that my former officemate Andreas Reinhart (University of Graz, Austria) has disproven the Ankeny-Artin-Chowla conjecture: more precisely, Andreas has found that $$ d := 331914313984493$$ is a counterexample to the conjecture, see https://arxiv.org/abs/2410.21864 (especially Theorem 2.3) for further details. This is not exactly an answer to the OP, but seems relevant nonetheless.

It appears that my former officemate Andreas Reinhart (University of Graz, Austria) has disproven the Ankeny–Artin–Chowla conjecture: more precisely, Andreas has found that $$ d := 331914313984493$$ is a counterexample to the conjecture, see A counterexample to the Conjecture of Ankeny, Artin and Chowla (especially Theorem 2.3) for further details. This is not exactly an answer to the OP, but seems relevant nonetheless.

It has been a long time since the question was asked. Nevertheless, it appears that my former officemate Andreas Reinhart (University of Graz, Austria) has disproven the Ankeny-Artin-Chowla conjecture, see https://arxiv.org/abs/2410.21864 for details. This is not exactly an answer to the OP, but seems relevant.

It appears that my former officemate Andreas Reinhart (University of Graz, Austria) has disproven the Ankeny-Artin-Chowla conjecture: more precisely, Andreas has found that $$ d := 331914313984493$$ is a counterexample to the conjecture, see https://arxiv.org/abs/2410.21864 (especially Theorem 2.3) for further details. This is not exactly an answer to the OP, but seems relevant nonetheless.

It has been a long time since this question was asked. Nevertheless, it appears that my former officemate Andreas Reinhart (University of Graz, Austria) has disproven the Ankeny-Artin-Chowla conjecture, see https://arxiv.org/abs/2410.21864 for details.

It has been a long time since the question was asked. Nevertheless, it appears that my former officemate Andreas Reinhart (University of Graz, Austria) has disproven the Ankeny-Artin-Chowla conjecture, see https://arxiv.org/abs/2410.21864 for details. This is not exactly an answer to the OP, but seems relevant.