  We study how stellar rotation curves (RCs) of galaxies are correlated on
average with morphology and stellar mass ($M_\mathrm{star}$) using the final
release of Sloan Digital Sky Survey IV MaNGA data. We use the visually assigned
$T$-types for the morphology indicator, and adopt a functional form for the RC
that can model non-flat RCs at large radii. We discover that within the radial
coverage of the MaNGA data, the popularly known flat rotation curve at large
radii applies only to the particular classes of galaxies, i.e., massive late
types ($T$-type $\geq1$, $M_\mathrm{star}\gtrsim10^{10.8}M_\odot$) and S0 types
($T$-type$=-1$ or $0$, $M_\mathrm{star}\gtrsim10^{10.0}M_\odot$). The RC of
late-type galaxies at large radii rises more steeply as $M_\mathrm{star}$
decreases, and its slope increases to about $+9$ km s$^{-1}$kpc$^{-1}$ at
$M_\mathrm{star}\approx10^{9.7}M_\odot$. By contrast, elliptical galaxies
($T$-type $\le-2$) have descending RCs at large radii. Their slope becomes more
negative as $M_\mathrm{star}$ decreases, and reaches as negative as $-15$ km
s$^{-1}$kpc$^{-1}$ at $M_\mathrm{star}\approx10^{10.2}M_\odot$. We also find
that the inner slope of the RC is highest for elliptical galaxies with
$M_\mathrm{star}\approx10^{10.5}M_\odot$, and decreases as $T$-type increases
or $M_\mathrm{star}$ changes away from $10^{10.5}M_\odot$. The velocity at the
turnover radius $R_t$ is higher for higher $M_\mathrm{star}$, and $R_t$ is
larger for higher $M_\mathrm{star}$ and later $T$-types. We show that the inner
slope of the RC is coupled with the central surface stellar mass density, which
implies that the gravitational potential of central regions of galaxies is
dominated by baryonic matter. With the aid of simple models for matter
distribution, we discuss what determines the shapes of RCs.
