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Full list of authors: Stock, S.; Nagel, E.; Kemmer, J.; Passegger, V. M.; Reffert, S.; Quirrenbach, A.; Caballero, J. A.; Czesla, S.; Béjar, V. J. S.; Cardona, C.; Díez-Alonso, E.; Herrero, E.; Lalitha, S.; Schlecker, M.; Tal-Or, L.; Rodríguez, E.; Rodríguez-López, C.; Ribas, I.; Reiners, A.; Amado, P. J.; Bauer, F. F.; Bluhm, P.; Cortés-Contreras, M.; González-Cuesta, L.; Dreizler, S.; Hatzes, A. P.; Henning, Th.; Jeffers, S. V.; Kaminski, A.; Kürster, M.; Lafarga, M.; López-González, M. J.; Montes, D.; Morales, J. C.; Pedraz, S.; Schöfer, P.; Schweitzer, A.; Trifonov, T.; Zapatero Osorio, M. R.; Zechmeister, M., We announce the discovery of two planets orbiting the M dwarfs GJ 251 (0.360 ± 0.015M-) and HD 238090 (0.578 ± 0.021M-) based on CARMENES radial velocity (RV) data. In addition, we independently confirm with CARMENES data the existence of Lalande 21185 b, a planet that has recently been discovered with the SOPHIE spectrograph. All three planets belong to the class of warm or temperate super-Earths and share similar properties. The orbital periods are 14.24 d, 13.67 d, and 12.95 d and the minimum masses are 4.0 ± 0.4 M-, 6.9 ± 0.9 M-, and 2.7 ± 0.3 M- for GJ 251 b, HD 238090 b, and Lalande 21185 b, respectively. Based on the orbital and stellar properties, we estimate equilibrium temperatures of 351.0 ± 1.4 K for GJ 251 b, 469.6 ± 2.6 K for HD 238090 b, and 370.1 ± 6.8 K for Lalande 21185 b. For the latter we resolve the daily aliases that were present in the SOPHIE data and that hindered an unambiguous determination of the orbital period. We find no significant signals in any of our spectral activity indicators at the planetary periods. The RV observations were accompanied by contemporaneous photometric observations. We derive stellar rotation periods of 122.1 ± 2.2 d and 96.7 ± 3.7 d for GJ 251 and HD 238090, respectively. The RV data of all three stars exhibit significant signals at the rotational period or its first harmonic. For GJ 251 and Lalande 21185, we also find long-period signals around 600 d, and 2900 d, respectively, which we tentatively attribute to long-term magnetic cycles. We apply a Bayesian approach to carefully model the Keplerian signals simultaneously with the stellar activity using Gaussian process regression models and extensively search for additional significant planetary signals hidden behind the stellar activity. Current planet formation theories suggest that the three systems represent a common architecture, consistent with formation following the core accretion paradigm. © ESO 2020., We thank the anonymous referee, whose comments improved this work. This work was supported by the DFG Research Unit FOR2544 "Blue Planets around Red Stars", project no. RE 2694/4-1. CARMENES is an instrument for the Centro Astronomico Hispano-Aleman (CAHA) at Calar Alto (Almeria, Spain), operated jointly by the Junta de Andalucia and the Instituto de Astrofisica de Andalucia (CSIC). CARMENES was funded by the Max-Planck-Gesellschaft (MPG), the Consejo Superior de Investigaciones Cientificas (CSIC), the Ministerio de Economia y Competitividad (MINECO) and the European Regional Development Fund (ERDF) through projects FICTS2011-02, ICTS-2017-07-CAHA-4, and CAHA16-CE-3978, and the members of the CARMENES Consortium (Max-Planck-Institut fur Astronomie, Instituto de Astrofisica de Andalucia, Landessternwarte Konigstuhl, Institut de Ciencies de l'Espai, Insitut fur Astrophysik Gottingen, Universidad Complutense de Madrid, Thuringer Landessternwarte Tautenburg, Instituto de Astrofisica de Canarias, Hamburger Sternwarte, Centro de Astrobiologia and Centro Astronomico Hispano-Aleman), with additional contributions by the Spanish Ministry of Economy, the German Science Foundation through the Major Research Instrumentation Program and DFG Research Unit FOR2544 "Blue Planets around Red Stars", the Klaus Tschira Stiftung, the states of Baden-Wurttemberg and Niedersachsen, and by the Junta de Andalucia. We acknowledge financial support from the Agencia Estatal de Investigacion of the Ministerio de Ciencia, Innovacion y Universidades and the ERDF through projects PID2019-109522GB-C51/2/3/4 PGC2018-098153-B-C33 AYA2016-79425-C3-1/2/3-P, ESP2016-80435-C2-1R, and the Centre of Excellence "Severo Ochoa" and "Maria de Maeztu" awards to the Instituto de Astrofisica de Canarias (SEV-2015-0548), Instituto de Astrofisica de Andalucia (SEV-2017-0709), and Centro de Astrobiologia (MDM2017-0737), the Generalitat de Catalunya/CERCA programme, and the NASA Grant NNX17AG24G. LCOGT observations were partially acquired via program number TAU2019A-002 of the Wise Observatory, Tel-Aviv University, Israel. This paper includes data collected by the TESS mission, which are publicly available from the Mikulski Archive for Space Telescopes (MAST). The analysis of this work has made use of a wide variety of public available software packages that are not referenced in the manuscript: Exo-Striker (Trifonov 2019), astropy Astropy Collaboration (2018), scipy (Virtanen et al. 2020), numpy (Oliphant 2006), matplotlib (Hunter 2007), tqdm (da Costa-Luis 2019), pandas (The pandas development team 2020), and seaborn (Waskom et al. 2020).