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Context. The Javalambre Photometric Local Universe Survey (J-PLUS) is an observational campaign that aims to obtain photometry in 12 ultraviolet-visible filters (0.3-1 μm) over ∼8500 deg2 of the sky observable from Javalambre (Teruel, Spain). Due to its characteristics and observation strategy, this survey will allow a great number of Solar System small bodies to be analyzed, and with improved spectrophotometric resolution with respect to previous large-area photometric surveys in optical wavelengths. Aims. The main goal of the present work is to present the first catalog of magnitudes and colors of minor bodies of the Solar System compiled using the first data release (DR1) of the J-PLUS observational campaign: the Moving Objects Observed from Javalambre (MOOJa) catalog. Methods. Using the compiled photometric data we obtained very-low-resolution reflectance (photo)spectra of the asteroids. We first used a σ-clipping algorithm in order to remove outliers and clean the data. We then devised a method to select the optimal solar colors in the J-PLUS photometric system. These solar colors were computed using two different approaches: on one hand, we used different spectra of the Sun convolved with the filter transmissions of the J-PLUS system, and on the other, we selected a group of solar-type stars in the J-PLUS DR1 according to their computed stellar parameters. Finally, we used the solar colors to obtain the reflectance spectra of the asteroids. Results. We present photometric data in the J-PLUS filters for a total of 3122 minor bodies (3666 before outlier removal), and we discuss the main issues with the data, as well as some guidelines to solve them. © ESO 2021. ; DM acknowledges the CNPq for the support in form of a PCI grant, and also the FAPERJ for the support in the form of a Pós-Doutorado Nota 10 grant. JMC acknowledges CPNq for support through a research fellowship. AAC acknowledges support from FAPERJ (grant E26/203.186/2016) and CNPq (grants 304971/2016-2 and 401669/2016-5), from the Universidad de Alicante under contract UATALENTO18-02, and from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709) MDP ackowledges funding by the Preeminent Postdoctoral Program (P3) at the University of Central Florida. JL acknowledges support from the project AYA2015-67772-R (MINECO). AG acknowledges CAPES for the support in the form of a Phd. grant. MM acknowledges funding by the European Space Agency under the research contract C4000122918. ESM and FJE acknowledge funding by the Spanish State Research Agency (AEI) Projects AYA2017-84089 and MDM-2017-0737 at Centro de Astrobiología (CSIC-INTA), Unidad de Excelencia María de Maeztu. The present work is based on observations made with the JAST/T80 telescope for the J-PLUS project at the Observatorio Astrofísico de Javalambre in Teruel, a Spanish Infraestructura Cientifico-Técnica Singular (ICTS) owned, managed and operated by the Centro de Estudios de Física del Cosmos de Aragón (CEFCA). Data has been processed and provided by CEFCA's Unit of Processing and Archiving Data (UPAD). Funding for the J-PLUS Project has been provided by the Governments of Spain and Aragón through the Fondo de Inversiones de Teruel; the Aragón Government through the Research Groups E96, E103, and E16_17R; the Spanish Ministry of Science, Innovation and Universities (MCIU/AEI/FEDER, UE) with grants PGC2018-097585-B-C21 and PGC2018-097585-B-C22; the Spanish Ministry of Economy and Competitiveness (MINECO) under AYA2015-66211-C2-1-P, AYA2015-66211-C2-2, AYA2012-30789, and ICTS-2009-14; and European FEDER funding (FCDD10-4E-867, FCDD13-4E-2685). The Brazilian agencies FAPESP and the National Observatory of Brazil have also contributed to this project. ; Peer reviewed