#### Recommended Citation

Postprint version. Published in *Journal of Number Theory*, Volume 15, Issue 3, December 1, 1982, pages 318-330.

The definitive version is available at https://doi.org/10.1016/0022-314X(82)90036-1.

#### Abstract

Let O=lim_{n}Z/p^{n}Z, , let A=O[g_{2},g_{3}] Δ, where g_{2} and g_{3} are coefficients of the elliptic curve: Y^{2} = 4X^{3} − g_{2}X − g_{3} over a finite field and Δ = g_{2}^{3} − 27g_{3}^{2} and let B=A[X,Y]/(Y^{2}-4X^{3}+g_{2}X+g_{3}). Then the p-adic cohomology theory will be applied to compute explicitly the zeta matrices of the elliptic curves, induced by the pth power map on the free AzQ -module H1(X, AzQ). Main results are; Theorem 1.1: X^{2} dY and Y dX are basis elements for H^{1}(X, IA(X)zQ); Theorem 1.2: Y dX, X^{2} dY, Y−1 dX, Y−2 dX and XY−2 dX are basis elements for H^{1}(X – (Y=0) IA(X)zQ), where X is a lifting of X, and all the necessary recursive formulas for this explicit computation are given.

#### Disciplines

Mathematics

#### Copyright

1982 Elsevier.

**URL:** http://digitalcommons.calpoly.edu/math_fac/39