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A standard theorem about finitely generated abelian groups tells us that E(ℚ) looks like qquad E(ℚ)≅( mbox FiniteGroup)⨯ underbrace {ℤ⨯ℤ⨯...⨯{Z_(r mbox copies) qquad E(ℚ)≅E(ℚ)(mbox tors)⨯ underbrace ℤ⨯ℤ⨯...⨯ℤ(r mbox copies) The finite subgroup E(ℚ)_(mbox tors) is called the qquad color red mbox TorsionSubgroupofE(ℚ).}}

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