Lemma 4.5. Assuming that:

  • char⁡K≠2

  • E: y2=f(x)=(x−e1)(x−e2)(x−e3), e1,e2,e3∈K¯

Then E[2]={0E,(e1,0),(e2,0),(e3,0)}≅(ℤ∕2ℤ)2.