| We first find upper bounds for the degrees of the coordinate functions of the elliptic Teichmuller lift of an ordinary elliptic curve over a perfect field of characteristic p > 0, giving exact conditions for the bound to be achieved. Also, we give an algorithm to compute the reduction modulo p3 of the canonical lift and the elliptic Teichmuller.; Next, motivated by coding theory, we look for lifts with degrees smaller than the degrees of the elliptic Teichmuller, finding again some upper bounds. We obtain some more precise information about those lifts modulo p3, such as precise degrees and verify that we can lift of the Frobenius on the affine parts. We again show how to compute those lifts.; We then compute lifts of hyperelliptic curves with "small" degrees, give a lower bound for these degrees and conditions to achieve this bound. Finally, we give an example of a lift that is possibly a Mochizuki lift. |
