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In this paper, we show that the Mordell-Weil group of the Weierstrass equation      y 2 = x ( x −  1 ) ( x −  t 2 −  c ) , c ≠  0 , 1 {y^2}\, = \,x(x\, - \,1)(x\, - \,{t^2}\, - \,c),\,c \ne \,0,\,1       (i.e., the group of solutions ( x,y ), with      x , y ∈  C ( t ) x,\,y\, \in \,{\textbf {C}}(t)      ) is generated by its elements of order 2, together with one element of infinite order, which is exhibited.

The group of rational solutions of 𝑦²=𝑥(𝑥-1)(𝑥-𝑡²-𝑐)