This question is a homework problem, and I'm having a lot of trouble with it.
(a) Determine the number of isomorphism classes of function fields K of degree 3 over $F = \mathbb{C}(t)$ that are ramified only at the points 1 and -1.
Is it just the number of different ways to glue together 3 sheets with two different branch cuts? Any help would be very much appreciated. Thanks!
I think the number is 3.
(a) $\sigma_1$(1,2,3), $\sigma_{-1}$(1,2,3), $f(t,x) = x^3 - (t^2 -1)$
(b) $\sigma_1$(1,2), $\sigma_{-1}$(2,3), $f(t,x) = x^3 -3x + 2t$
(C) $\sigma_1$(1,2,3), $\sigma_{-1}$(2,3), $f(t,x) = x^3 + 2tx^2 - tx$