<p>Encoding of protein-coding sequences in a genome through evolution leads to characteristic proportions of codons and amino acids. Here, we present a simplified maximum entropy model that groups together codons with the same GC (guanine + cytosine) content and coding for the same amino acid and accounts for the stoichiometry of genetic elements in over 50000 genomes with seven interpretable parameters. Our model includes both the cost of a codon given a genomic GC content and the metabolic cost of the corresponding amino acid. Both costs are essential for accurate prediction of codon and amino acid abundances. The best implementation of the model includes a universal equilibrium value for the genomic GC content below 50%, as suggested by the literature. It also splits the twenty amino acids in two groups forming strong (bases C and G) or weak (bases A and U) Watson Crick base pairs with the anticodon, differing in the strength of GC-dependent selection. The entropy-cost trade-off suggests that each organism has sorted out the genome encoding problem given a value for its genomic GC content. The empirical boundaries to this trade-off suggest minimal values for the amino acid and codon entropies, which may limit the GC content of natural genomes.</p>