Legendre Drinfeld modules and universal supersingular polynomials

Ahmad El-Guindy

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arXiv · 1308.0855

Legendre Drinfeld modules and universal supersingular polynomials

Ahmad El-Guindy

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Abstract

We introduce a certain family of Drinfeld modules that we propose as analogues of the Legendre normal form elliptic curves. We exhibit explicit formulas for a certain period of such Drinfeld modules as well as formulas for the supersingular locus in that family, establishing a connection between these two kinds of formulas. Lastly, we also provide a closed formula for the supersingular polynomial in the $\jmath$-invariant for generic Drinfeld modules.

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Ahmad El-Guindy. 2013-08-04. Legendre Drinfeld modules and universal supersingular polynomials. https://arxiv.org/abs/1308.0855

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