Involutory elliptic curves over
For let be a subgroup of the Atkin-Lehner involutions of the Drinfeld modular curve . We determine all and for which the quotient curve is rational or elliptic.
For let be a subgroup of the Atkin-Lehner involutions of the Drinfeld modular curve . We determine all and for which the quotient curve is rational or elliptic.
We explicitly determine the elliptic surfaces with section and maximal singular fibre. If the characteristic of the ground field is different from , for each of the two possible maximal fibre types, and , the surface is unique. In characteristic the maximal fibre types are and , and there exist two (resp. one) one-parameter families of such surfaces.
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