Open Access
November 2013 Explicit $t$-expansions for the elliptic curve $y^{2}= 4(x^{3}+Ax+B)$
Seidai Yasuda
Proc. Japan Acad. Ser. A Math. Sci. 89(9): 123-127 (November 2013). DOI: 10.3792/pjaa.89.123


For an elliptic curve $E: y^{2} = 4(x^{3} + A x +B)$ over a field of characteristic $\neq 2$, we explicitly compute the pullback to the formal completion of $E$ at the origin of some important objects on $E$ including the functions $x$, $y$ and the invariant differential $\omega=dx/y$ in terms of the formal parameter $t = -2x/y$.


Download Citation

Seidai Yasuda. "Explicit $t$-expansions for the elliptic curve $y^{2}= 4(x^{3}+Ax+B)$." Proc. Japan Acad. Ser. A Math. Sci. 89 (9) 123 - 127, November 2013.


Published: November 2013
First available in Project Euclid: 30 October 2013

zbMATH: 1286.14048
MathSciNet: MR3127931
Digital Object Identifier: 10.3792/pjaa.89.123

Primary: 14H52
Secondary: 33C75 , 33E05

Keywords: Elliptic curves , invariant differential , Sigma Function

Rights: Copyright © 2013 The Japan Academy

Vol.89 • No. 9 • November 2013
Back to Top