A Kuribayashi quartic curve ca : X-4 + Y-4 + Z(4) + a((XY2)-Y-2 + Y(2)Z(2) + Z(2)X(2)) = 0, a is an element of C{-1, +/- 2}, carries total sextactic points if and only if a = 14 or a is a zero of P(a) = a(3) + 68a(2) - 91a + 98, cf. 1. In 2, the authors describe the subgroup generated by the total sextactic points in the Jacobian of a Kuribayashi quartic curve when a is a zero of P(a). In this paper, we describe this group when a = 14.
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