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Aims: We aim to study the temporal and spectral behaviour of the eclipsingpolar CSS081231:071126+440405 from the infrared to the X-ray regime.  Methods: We obtained phase-resolved XMM-Newton X-ray observations on twooccasions in 2012 and 2013 in different states of accretion. In 2013 theXMM-Newton X-ray and UV data were complemented by optical photometric andspectroscopic observations.  Results: CSS081231 displays two-pole accretion in the high state. Themagnetic fields of the two poles are 36 and 69 MG, indicating a non-dipolarfield geometry. The X-ray spectrum of the main accreting pole with the lowerfield comprises a hot thermal component from the cooling accretion plasma,$kT_{plas}$ of a few tens of keV, and a much less luminous blackbody-likecomponent from the accretion area with $kT_{\rm bb} \sim$ 50-100\,eV. Thehigh-field pole which was located opposite to the mass-donating star accretesat a low rate and has a plasma temperature of about 4\,keV. At both occasionsthe X-ray eclipse midpoint precedes the optical eclipse midpoint by 3.2seconds. The center of the X-ray bright phase shows accretion-rate dependentlongitudinal motion of ~20 degrees.  Conclusions: CSS081231 is a bright polar that escaped detection in the RASSsurvey because it was in a low accretion state. Even in the high state it lacksthe prominent soft component previously thought ubiquitous in polars. Such anexcess may still be present in the unobserved extreme ultraviolet. All polarsdiscovered in the XMM-Newton era lack the prominent soft component. Theintrinsic spectral energy distribution of polars still awaits characterisationby future X-ray surveys such as eROSITA. The trajectory taken by material toreach the second pole is still uncertain.

XMM-Newton and optical observations of the eclipsing polar CSS081231:071126+440405