Mazur's torsion theorem

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In algebraic geometry Mazur's torsion theorem, due to Barry Mazur, classifies the possible torsion subgroups of the group of rational points on an elliptic curve defined over the rational numbers.

If C_n denotes the cyclic group of order n, then the possible torsion subgroups are C_n with 1 ≤ n ≤ 10, and also C₁₂; and the direct sum of C₂ with C₂, C₄, C₆ or C₈.

[edit] References

Mazur, Barry: Rational isogenies of prime degree, Inventiones Math. 44 (1978), pp 129-162.