Curves over finite fields attain the Hallouin-Perret quadratic-extension bound exactly when all real parts of their Frobenius eigenvalues coincide, which yields new coefficient bounds and low-genus classifications.
An exhaustive com- puter search for finding new curves with many points among fibre products of two Kummer covers over F5 and F7
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Maximal curves with respect to quadratic extensions over finite fields
Curves over finite fields attain the Hallouin-Perret quadratic-extension bound exactly when all real parts of their Frobenius eigenvalues coincide, which yields new coefficient bounds and low-genus classifications.