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Let Eq: y2 + XY = X3 + h4X + h6 be the Tate curve with canonical differential, w = dX/(2Y + X). If the characteristic is p > 0, then the Hasse invariant, H, of the pair (Eq, w) should equal one. If p > 3, then calculation of H leads to a nontrivial separable relation between the coefficients h4 and h6. If p = 2 or p = 3, Thakur related h4 and h6 via elementary methods and an identity of Ramanujan. Here, we treat uniformly all characteristics via explicit calculation of the formal group law of Eq. Our analysis was motivated by the study of the invariant A which is an infinite Witt vector generalizing the Hasse invariant.

Congruences between the coefficients of the Tate curve via formal groups