We present the discovery of NGTS J214358.5-380102, an eccentric M-dwarf binary discovered by the Next Generation Transit Survey. The system period of 7.618 days is greater than many known eclipsing M-dwarf binary systems. Its orbital eccentricity of $0.323^{+0.0014}_{-0.0037}$, is large relative to the period and semi-major axis of the binary. Global modelling of photometry and radial velocities indicate stellar masses of $M_A$=$0.426 ^{+0.0056}_{-0.0049}$, $M_B$=$0.455 ^{+0.0058}_{-0.0052}$ and stellar radii $R_A$=$0.461 ^{+0.038}_{-0.025}$ $R_B$=$0.411 ^{+0.027}_{-0.039}$, respectively. Comparisons with stellar models for low mass stars show that one star is consistent with model predictions whereas the other is substantially oversized. Spectral analysis of the system suggests a primary of spectral type M3V, consistent with both modelled masses and radii, and with SED fitting of NGTS photometry. As the most eccentric eclipsing M-dwarf binary known, NGTS J214358.5-380102 provides an interesting insight into the strength of tidal effects in the circularisation of stellar orbits.
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