If we are given an elliptic curve of the form $y^2 = (x-e_1)(x-e_2)(x-e_3) $, where $ e_1 > e_2 > e_3 $ and all $ e_i $ are real, then we can evaluate the period and the dual period, which will be Gauss hypergeometric functions.

My question is: if we are given a hypergeometric function $ _2 F_1 (a,b,c;z)$, is it possible to directly get the elliptic function whose periods are this hypergeometric function? More precisely, is there a way in which, given $(a,b,c)$, we can determine $(e_1,e_2,e_3)$?