Abstract
<p> Li, Mantovan, Pries, and Tang proved the existence of supersingular curves over <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper F Subscript p Baseline overbar"> <mml:semantics> <mml:mover> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">F</mml:mi> </mml:mrow> <mml:mi>p</mml:mi> </mml:msub> <mml:mo accent="false"> ¯ </mml:mo> </mml:mover> <mml:annotation encoding="application/x-tex">\overline {\mathbb {F}_p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in each of the special families of curves in Moonen’s classification. Their proof does not provide defining equations of these curves. We make some of their results explicit using the reductions modulo <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of previously computed curves with complex multiplication. </p>