We address consequences of strong tensor and weak spin-orbit terms in the local energy density functional, resulting from fits to the $f_{5/2} - f_{7/2}$ splittings in $^{40}$Ca, $^{48}$Ca, and $^{56}$Ni. In this study, we focus on nuclear binding energies. In particular, we show that the tensor contribution to the binding energies exhibits interesting topological features closely resembling that of the shell-correction. We demonstrate that in the extreme single-particle scenario at spherical shape, the tensor contribution shows tensorial magic numbers equal to $N(Z)$=14, 32, 56, and 90, and that this structure is smeared out due to configuration mixing caused by pairing correlations and migration of proton/neutron sub-shells with neutron/proton shell filling. Based on a specific Skyrme-type functional SLy4$_T$, we show that the proton tensorial magic numbers shift with increasing neutron excess to $Z$=14, 28, and 50.
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