Data related to

"On the Integral Cohomology of Bianchi groups"

The following Excel files contain data about the abelianization G of the congruence subgroups of type Gamma_0 with split prime level for the five Euclidean Bianchi groups. In column A, we see the norm of the level of G. Column B is the ratio of log(size of torsion part of G) versus the volume of the associated 3-fold. This is related to the work of Bergeron-Venkatesh. Column C holds the torsion-free rank of G. The Excel files also contain the statistics coming from the first 3 columns but these statistics are already present in the paper. Finally, the Excel file for d=-1 contains the list of the norms of the primes related to the conjecture of Long-MacLachlan-Reid. Please consult the paper for details.

Excel file for the Bianchi group with d=-1.

Excel file for the Bianchi group with d=-2.

Excel file for the Bianchi group with d=-3.

Excel file for the Bianchi group with d=-7.

Excel file for the Bianchi group with d=-11.


To get a taste of the sporadic and astronomical nature of the torsion in the above mentioned abelianizations G, take a look at the below text files. The first entry of each line is the norm of the level of G. The sequence that follows is the list of primes that divide the size of the torsion part of G, except that the first entry of the sequence is the torsion-free rank of G.

Torsion in the case d=-1.

Torsion in the case d=-2.

Torsion in the case d=-3.

Torsion in the case d=-7.

Torsion in the case d=-11.