Abstract. We have investigated the neutrino induced coherent pion production reaction at the energies of interest for recent experiments like K2K and MiniBooNE. The model includes pion, nucleon and the ∆(1232) resonance. Medium effects in the production mechanism and the distortion of the pion wave function are taken into account. We find a strong reduction of the cross section due to these effects and also substantial modifications in the energy distributions of the final pion. The sensitivity of the results on the axial N-∆ coupling C A 5 (0) and the coherent fraction in neutral-current π 0 production are discussed.Keywords: Neutrino-nucleus interactions, N-∆ form factors, Pions in the nuclear medium PACS: 25.30. Pt, 13.15.+g, 23.40.Bw The coherent production of pions in charged current (CC) and neutral current (NC) processes is a subject of research in current and future experiments. The K2K collaboration has not found any evidence of ν µ + 12 C → µ − + π + + 12 C, obtaining an upper limit for the coherent fraction over the total CC interaction [1] well below the estimates based on the Rein and Sehgal model [2]. On the other side, preliminary MiniBooNE results indicate that part of the NC π 0 production comes from the coherent reaction ν + 12 C → ν + π 0 + 12 C [3]. In future, the SciBooNE detector [4] should be able to identify π 0 's emitted in the forward direction, where most of the coherent events are concentrated, while MINERνA [5] will collect data with high statistics, allowing for a clear separation between coherent and incoherent processes and the comparison between neutrino and antineutrino cross sections.Since the pioneering work of Ref.[2] some other studies focused on the energy region ∼ 1 GeV, where the modification of the ∆(1232) spectral function inside the nuclear medium is relevant [6,7,8]. Pion distortion is taken into account in Refs. [2,9] by factorizing the pion-nucleus elastic cross section (c.s.). In a more general fashion, it can be incorporated in the amplitude by means of the distorted wave Born approximation, using a pion wave function obtained in the eikonal limit [8] or by solving the KleinGordon equation with a realistic optical potential [7].We have performed a theoretical study of neutrino induced coherent pion [10, 11] production extending and improving the calculations of Refs. [7,8]. The model is built in terms of the relevant hadronic degrees of freedom: pion, nucleon and ∆ resonance. Besides the dominant direct ∆ excitation, it includes the crossed ∆ and nucleon-pole terms [11] (see the left panel of Fig. 1). There are other contributions allowed by chiral symmetry [12] but they cancel for isospin symmetric nuclei, so we neglect them.The relativistic amplitude is proportional to the product of the standard leptonic