Galois group at Galois point for genus-one curve

Details Galois group at Galois point for genus-one curve Galois group at Galois point for genus-one curve

2011-05-09

arxiv.org/abs/1105.1602v1

Mathematics

Number Theory

Scientific paper

We show all the possible structures of finite subgroups of the automorphism groups of elliptic curves. Here the automorphism means the biholomorphic transformation. Using the result, we determine every Galois group G at outer Galois point for genus-one curve with singular points. In particular, if G is abelian, then its order is at most nine. However if not so, the order is unbounded. Furthermore, we give every defining equation of the curve with the Galois point in the case where G is abelian.

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