We present H \alpha rotation curves of two low luminosity field galaxies with r -band absolute magnitudes M _ { r } = -13.9 ^ { +0.8 } _ { -0.5 } and M _ { r } = -14.7 ^ { +0.3 } _ { -0.2 } ( for h \equiv H _ { 0 } / 100 { km } { s } ^ { -1 } { Mpc } ^ { -1 } = 0.7 ; the large error bars reflect distance uncertainties ) . Most previously studied galaxies in this luminosity range are members of groups defined by brighter galaxies , but these two systems , selected from Blanton et al. ’ s ( 2004 ) sample of low luminosity galaxies in the Sloan Digital Sky Survey ( SDSS ) , appear to have no bright companions . The measured rotation speeds at the outer extent of the H \alpha rotation curves , 34.8 \pm 3.8 { km } { s } ^ { -1 } and 30.9 \pm 7.2 { km } { s } ^ { -1 } , are larger than the values of 16.0 ^ { +6.1 } _ { -5.4 } { km } { s } ^ { -1 } and 20.9 ^ { +6.2 } _ { -5.2 } { km } { s } ^ { -1 } predicted by extrapolating the inverse Tully-Fisher relation of luminous SDSS galaxies to these faint luminosities . However , a previous HI measurement of the first galaxy shows that it has a gas mass similar to its stellar mass , and the total baryonic mass is consistent with that predicted by McGaugh et al. ’ s ( 2000 ) “ baryonic Tully-Fisher relation. ” We find r -band dynamical mass-to-light ratios within the radii of the last H \alpha data points ( about 1.8 disk scale lengths in each case ) of 12.6 ^ { +4.7 } _ { -4.5 } M _ { \odot } / L _ { \odot } and 4.8 _ { -2.1 } ^ { +2.5 } M _ { \odot } / L _ { \odot } , much higher than the values \sim 1 M _ { \odot } / L _ { \odot } expected for the stellar populations . The dynamical properties of these galaxies , including the rotation speeds and evidence for high gas fractions and dark matter domination within the luminous extent of the galaxy , are consistent with those of previously studied faint galaxies in nearby groups . Further studies of the SDSS sample will allow characterization of low luminosity galaxies over the full range of environments in which they reside .