Bounds for Integral j -Invariants and Cartan Structures on Elliptic Curves

Details Bounds for Integral j -Invariants and Cartan Structures on Elliptic Curves Bounds for Integral j -Invariants and Cartan Structures on Elliptic Curves

2008-07-15

arxiv.org/abs/0807.2350v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We bound the j -invariant of integral points on a modular curve in terms of
the congruence group de?ning the curve. We apply this to prove that the modular
curve Xsplit (p3) has no non-trivial rational point if p is a sufficiently
large prime number. Assuming the GRH, one can replace p3 by p2 .

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