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Elliptic
Mars, and all the other planets, have oval-shaped, or eliptical, orbits.
Generally speaking, yes. It should be noted however that the outer planets have a more elliptic orbit (egg shaped).
Riemann created elliptic geometry in 1854.
A modular elliptic curve is a type of elliptic curve E that allows for the parametrization of X0(N) -> E through a modular curve.