Login
This is a place holder for potential sponsor logos.
Mazur's theorem on torsion of elliptic curves
Theorem 1 (Mazur) Let $E/\Rats$ be an elliptic curve. Then the torsion subgroup $E_{\operatorname{torsion}}(\Rats)$ is exactly one of the following groups: $$\Ints/N\Ints \quad 1\leq N \leq 10\quad or\quad N=12$$ $$\Ints /2 \Ints \oplus \Ints / 2N \Ints \quad 1\leq N\leq 4$$
Note: see Nagell-Lutz theorem for an efficient algorithm to compute the torsion subgroup of an elliptic curve defined over $\Rats$ .
Bibliography
- 1
- Joseph H. Silverman, The Arithmetic of Elliptic Curves. Springer-Verlag, New York, 1986.
- 2
- Barry Mazur, Modular curves and the Eisenstein ideal, IHES Publ. Math. 47 (1977), 33-186.
- 3
- Barry Mazur, Rational isogenies of prime degree, Invent. Math. 44 (1978), 129-162.
Mazur's theorem on torsion of elliptic curves is owned by alozano.
None.