Predicting large scale conformations of protein structures is computationally demanding. Here we compute the conformation and elasticity of double-stranded coiled coils using a simple coarse-grained elastic model. By maximizing the contact between hydrophobic residues and minimizing the elastic energy, we show that the minimum energy structure of a coiled coil is a supercoiled double helix of alpha helices. For realistic binding energies, the elastic energy of the alpha helices requires binding every 7th residue, which leads to a pitch and helix angle for the structure that is consistent with experimental measurements. Analysis of the model equations shows how the pitch varies with the helical repeat of the hydrophobic residues and with the ratio of the twisting modulus to the bending modulus and provides an estimate of the persistence length of around 150 nm, in agreement with previous experimental estimates.