The amyloid cascade hypothesis states that senile plaques, composed of amyloid β (Aβ) fibrils, play a key role in Alzheimer's disease (AD). However, recent experiments have shown that Aβ oligomers are more toxic to neurons than highly ordered fibrils. The molecular mechanism underlying this observation remains largely unknown. One of the possible scenarios for neurotoxicity is that Aβ peptides create pores in the lipid membrane that allow Ca2+ ions to enter cells, resulting in a signal of cell apoptosis. Hence, one might think that oligomers are more toxic due to their higher ability to create ion channels than fibrils. In this work, we study the effect of Aβ42 dodecamer and fibrils on a neuronal membrane, which is similar to that observed in AD patients, using all-atom molecular dynamics simulations. Due to short simulation times, we cannot observe the formation of pores, but useful insight on the early events of this process has been obtained. Namely, we showed that dodecamer distorts the lipid membrane to a greater extent than fibrils, which may indicate that ion channels can be more easily formed in the presence of oligomers. Based on this result, we anticipate that oligomers are more toxic than mature fibrils, as observed experimentally. Moreover, the Aβ-membrane interaction was found to be governed by the repulsive electrostatic interaction between Aβ and the ganglioside GM1 lipid. We calculated the bending and compressibility modulus of the membrane in the absence of Aβ and obtained good agreement with the experiment. We predict that the dodecamer will increase the compressibility modulus but has little effect on the bending modulus. Due to the weak interaction with the membrane, fibrils insignificantly change the membrane elastic properties.