There are exactly 24 isomorphism classes of elliptic curves defined over Q with good reduction away from 2, classified by Ogg (1966).
There are 4 curves with j-invariant 128 given by y^2 = x^3 + x^2 + x + 1, y^2 = x^3 + x^2 + 3x - 5, y^2 = x^3 - x^2 + x - 1, and y^2 = x^3 - x^2 + 3x + 5.
There are 8 curves with j-invariant 1728 given by y^2 = x^3 - x, y^2 = x^3 + 4x, y^2 = x^3 - 4x, y^2 = x^3 + x, y^2 = x^3 - 2x, y^2 = x^3 + 8x, y^2 = x^3 -8x, and y^2 = x^3 + 2x.
There are 4 curves with j-invariant 8000 given by y^2 = x^3 + x^2 - 13x - 21, y^2 = x^3 + x^2 - 3x + 1, y^2 = x^3 - x^2 - 13x + 21, and y^2 = x^3 - x^2 - 3x - 1.
There are 4 curves with j-invariant 10976 given by y^2 = x^3 + x^2 - 9x + 7, y^2 = x^3 + x^2 - 2x - 2, y^2 = x^3 - x^2 - 9x - 7, and y^2 = x^3 - x^2 - 2x + 2.
There are 4 curves with j-invariant 287496 given by y^2 = x^3 - 11x - 14, y^2 = x^3 - 11x + 14, y^2 = x^3 - 44x - 112, and y^2 = x^3 - 44x + 112. (End)
