On the evaluation of modular polynomials

We present two algorithms that, given a prime ell and an elliptic curve E/Fq, directly compute the polynomial Phi_ell(j(E),Y) in Fq[Y] whose roots are the j-invariants of the elliptic curves that are ell-isogenous to E. We do not assume that the modular polynomial Phi_ell(X,Y) is given. The algorithms may be adapted to handle other types of modular polynomials, and we consider applications to point counting and the computation of endomorphism rings. We demonstrate the practical efficiency of the algorithms by setting a new point-counting record, modulo a prime q with more than 5,000 decimal digits, and by evaluating a modular polynomial of level ell = 100,019.Comment: 19 pages, corrected a typo in equation (8) and added equation (9

Management of threatened Aphanius Fasciatus at Il-Maghluq, Malta

Over the last decade the distribution of Aphanius fasciatus Nardo has regressed sharply across the Maltese Islands despite numerous legal conservation instruments. In this study we present the results of a one-year phenological study at the protected wetland site known as Il-Maghluq. The A. fasciatus population structure and a number of water physical characteristics were monitored. The biotic data collected was found to be consistent with that of a highly vulnerable population. The authors make a number of management recommendations to improve the conservation status of this population.peer-reviewe

History of Women’s Fellowship of Valley of Virginia, ca. 1964

Typed history created from organizational annuals and secretary books from 1938 - 1964 that describes the history of women\u27s missionary work in the Virginia Valley Central Congregational Christian Conference

Program Booklet for Women\u27s Fellowship 1972-1973, 1972

Annual program booklet of the Women\u27s Fellowship Committee. Includes officers, committee members, and monthly assignments

Program Booklet for Lay Life and Work 1965-1966, 1965

Annual program booklet of the Women\u27s Fellowship Committee. Includes officers, committee members, and monthly assignments

Church Record Book, 1910-1952

Ledger contains administrative records of the church including membership lists, lists of officers, business meeting minutes, and financial records. The bulk of the meeting minutes are from 1910-1933, and the membership lists date from 1920 - 1950s

Program Booklet for Lay Life and Work 1971-1972, 1971

Annual program booklet of the Women\u27s Fellowship Committee. Includes officers, committee members, and monthly assignments

Program Booklet for Women\u27s Fellowship, 1974-1975, 1974

Annual program booklet of the Women\u27s Fellowship Committee. Includes officers, committee members, and monthly assignments

Sunday School Account Book, 1913-1916

Ledger contains a record of the cash account of the Sunday School collection. Includes meeting minutes of the Sunday School Committee as well as a list of literature purchased for Sunday School and a few attendance lists