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Magma code for computing abelianizations of Gamma_0(I)

Magma code for computing Abelianizations of Gamma_0(I), congruence subgroup of PGL_2(O_K), where $O_K$ is the ring of integers of a quadratic imaginary number field. The code is an adaptation of previous code that was kindly provided to me by Haluk Sengun. It makes essential use of the program KleinianGroups written by Aurel Page to compute presentations of PGL_2(O_K). The latest version of KleinianGroups can be downloaded from Aurel's webpage .


Output of runs of this algorithm when K is an imaginary quadratic of class number one and I is a small power of a prime in K that lies above 2. These computations are used in the author's paper "On Fermat's equation over some small quadratic imaginary number fields" and the author's thesis.

K = Q(i), Q(sqrt(-2)), Q(sqrt(-3)), Q(sqrt(-7)), Q(sqrt(-11)), Q(sqrt(-19)), Q(sqrt(-43)), Q(sqrt(-67)) and Q(sqrt(-163))