Displaying similar documents to “Rational points on twists of X₀(63)”

The arithmetic of curves defined by iteration

Wade Hindes (2015)

Acta Arithmetica

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We show how the size of the Galois groups of iterates of a quadratic polynomial f can be parametrized by certain rational points on the curves Cₙ: y² = fⁿ(x) and their quadratic twists (here fⁿ denotes the nth iterate of f). To that end, we study the arithmetic of such curves over global and finite fields, translating key problems in the arithmetic of polynomial iteration into a geometric framework. This point of view has several dynamical applications. For instance, we establish a maximality...

On families of 9-congruent elliptic curves

Tom Fisher (2015)

Acta Arithmetica

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We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over ℚ, i.e. pairs of non-isogenous elliptic curves over ℚ whose 9-torsion subgroups are isomorphic as Galois modules.

Miror Curves

Slavik Jablan (2001)

Visual Mathematics

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