Leterrier, Gauthier2022-03-282022-03-282022-03-282022-06-0110.1007/s40993-022-00321-0https://infoscience.epfl.ch/handle/20.500.14299/186601WOS:000770327900001We study the elliptic curves given by y(2) = x(3) + bx + t(3n+1) over global function fields of characteristic 3 ; in particular we perform an explicit computation of the L-function by relating it to the zeta function of a certain superelliptic curve u(3) + bu = v(3n+1). In this way, using the Neron-Tate height on the Mordell-Weil group, we obtain lattices in dimension 2.3(n) for every n >= 1, which improve on the currently best known sphere packing densities in dimensions 162 (case n = 4) and 486 (case n = 5). For n = 3, the construction has the same packing density as the best currently known sphere packing in dimension 54, and for n = 1 it has the same density as the lattice E-6 in dimension 6.Mathematicselliptic curvesfunction fieldsl-functionsmordell-weil groupsphere packingselliptic-curvescharacteristic-2ranktext::journal::journal article::research article