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Discrete aurora at Mars, characterized by their small spatial scale and tendency to form near strong crustal magnetic fields, are emissions produced by particle precipitation into the Martian upper atmosphere. Since 2014, Mars Atmosphere and Volatile EvolutioN's (MAVEN's) Imaging Ultraviolet Spectrograph (IUVS) has obtained a large collection of UV discrete aurora observations during its routine periapsis nightside limb scans. Initial analysis of these observations has shown that, near the strongest crustal magnetic fields in the southern hemisphere, the IUVS discrete aurora detection frequency is highly sensitive to the interplanetary magnetic field (IMF) clock angle. However, the role of other solar wind properties in controlling the discrete aurora detection frequency has not yet been determined. In this work, we use the IUVS discrete aurora observations, along with MAVEN observations of the upstream solar wind, to determine how the discrete aurora detection frequency varies with solar wind dynamic pressure, IMF strength, and IMF cone angle. We find that, outside of the strong crustal field region (SCFR) in the southern hemisphere, the aurora detection frequency is relatively insensitive to the IMF orientation, but significantly increases with solar wind dynamic pressure, and moderately increases with IMF strength. Interestingly however, although high solar wind dynamic pressures cause more aurora to form, they have little impact on the brightness of the auroral emissions. Alternatively, inside the SCFR, the detection frequency is only moderately dependent on the solar wind dynamic pressure, and is much more sensitive to the IMF clock and cone angles. In the SCFR, aurora are unlikely to occur when the IMF points near the radial or anti-radial directions when the cone angle (arccos( B x /| B |)) is less than 30° or between 120° and 150°. Together, these results provide the first comprehensive characterization of how upstream solar wind conditions affect the formation of discrete aurora at Mars., (© 2022 The Authors.)