참고문헌
-
H. Baaziz, Equations for the modular curve
$X_1(N)$ and models of elliptic curves with torsion points, Math. Comp. 79 (2010), 2371-2386. https://doi.org/10.1090/S0025-5718-10-02332-X - D. Husemoller, Elliptic curves, Second edition, Springer-Verlag, New York, 2004.
-
N. Ishida and N. Ishii, Generators and defining equation of the modular function field of the group
${\Gamma}_1(N)$ , Acta Arith. 101 (2002), 303-320. https://doi.org/10.4064/aa101-4-1 - D. Jeon, C.H. Kim and Y. Lee, Families of elliptic curves over cubic number fields with prescribed torsion subgroups, Math. Comp. 80 (2011), 579-591.
- M. A. Reichert, Explicit determination of nontrivial torsion structures of elliptic curves over quadratic number fields, Math. Comp. 46 (1986), 637-658. https://doi.org/10.1090/S0025-5718-1986-0829635-X
- Y. Yang, Defining equations of modular curves, Adv. Math. 204 (2006), 481-508. https://doi.org/10.1016/j.aim.2005.05.019