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Abstract In this article, we study the logarithmic Mahler measure of one-parameter family $$Q_\alpha=y^2+(x^2-\alpha x)y+x,$$ denoted by $\mathrm{m}(Q_\alpha)$. The zero loci Qα generically define elliptic curves Eα, which are 3-isogenous to Hessian curves. We particularly interested in case $\alpha\in (-1,3)$, has not been considered literature due certain subtleties. For α interval, establish...