In this work, the following theorem is proved. Let m be a negative integer containing no square divisors. Consider the quadratic field k(√m) and let ω1, ω2 be a basis of some ideal of this field, with the imaginary part of the ratio ω2/ω1 being positive. Furthermore, let ρ(u; ω1, ω2, ω3) be the well-known Weierstrass function (in what follows we will index the basis ω1, ω2 such that the ratio ω2/ω1 has a positive imaginary part), which satisfies the following differential equation