We study the Drinfeld modular curves arising from the Hecke congruence subgroups of SL₂(Fq[T]). Using a combinatorial method of Gekeler and Nonnengardt, we obtain a genus formula for these curves. In cases when the genus is one, we compute the Weierstrass equation of the corresponding curve.
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Franklin et al. (2024) studied this question.
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