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The authors have determined whether the points fixed by all the full and the partial Atkin–Lehner involutions W_Q on X₀(N) for N ≤ 50 are Weierstrass points or not.

The design is by using Lawittes's and Schoeneberg's theorems.

Finding all Weierstrass points on X₀(N) fixed by some Atkin–Lehner involutions. Besides, the authors have listed them in a table.

The Weierstrass points have played an important role in algebra. For example, in algebraic number theory, they have been used by Schwartz and Hurwitz to determine the group structure of the automorphism groups of compact Riemann surfaces of genus g ≥ 2. Whereas in algebraic geometric coding theory, if one knows a Weierstrass nongap sequence of a Weierstrass point, then one is able to estimate parameters of codes in a concrete way. Finally, the set of Weierstrass points is useful in studying arithmetic and geometric properties of X₀(N).

Let E be an elliptic curve with Weierstrass form y2=x3−px, where p is a prime number and let E[m] be its m-torsion subgroup. Let p1=(x1,y1) and p2=(x2,y2) be a basis for E[m], then we prove that ℚ(E[m])=ℚ(x1,x2,ξm,y1) in general. We also find all the generators and degrees of the extensions ℚ(E[m])/ℚ for m=3 and m=4.

This study aims to investigate the behavioural intention and adoption of internet banking (IB) among clients of local and foreign Islamic banks in Malaysia.

Survey questionnaires were distributed among the Islamic banks’ clients at two main states, namely, Kuala Lumpur and Selangor. The number of clients involved is 319 (n = 319). The data was analysed using the partial least square (PLS) and theoretically, the research framework in this study is guided by the unified theory of acceptance and use of technology 2 (UTAUT2).

The smart PLS analysis yielded three main outcomes, namely, the variables such as performance expectancy, effort expectancy, price value, facilitating conditions and habit have a positive influence over the behavioural intention and subsequently lead to the adoption of IB. The other two variables, namely, social influence and hedonic motivation were negatively-related and insignificant for behavioural intention. Third, this paper also noticed that facilitating conditions and habits have a direct relationship with the adoption of IB.

Based on the findings, Islamic banks can take necessary action to design a better policy to further accelerate the usage of IB among their client. By identifying those factors, this, perhaps, can allow Islamic banks to invest more ideas on those significant factors that influence their interest, and subsequently leads to good business to Islamic banks as the clients nowadays are looking for simplicity and convenience factors when using IB.

This research is expected to enhance existing literature on internet banking, especially in Islamic banking research on the technological edge. Limited research has been done in Malaysia, particularly on the intention and continuous adoption of IB in Islamic banks using the UTAUT2 framework. This would be breakthrough research in identifying factors that influence customers’ continuous adoption of IB.