This repo has following files and checks various claims in the manuscript "ON THE FACTORIZATION OF TWISTED L-VALUES AND 11-DESCENTS OVER C5-NUMBER FIELDS" of Celine Maistret and I:

• curves_K11.m
• curves_K31.m
• check_vis.m
• check_Lval_K11.m
• helper_funcs.m
• compute_Selmer_11.m

The files above have the following descriptions:

• curves_K11.m: curve data on LMFDB that acquire 11-torsion of Sha over the degree 5 field K that is the degree 5 subfield of 11th cyclotomic field.

• curves_K31.m: curve data on LMFDB that acquire 11-torsion of Sha over the degree 5 field K that is the degree 5 subfield of 31th cyclotomic field.

• check_vis.m: this file checks the claims in Section 2.2 in the manuscript

• check_Lval_K11.m: this file checks that the 11-part of the factorization of the special L-value ideal varies as conjectured in Conjecture 1.3 in the manuscript w.r.t the Galois action on Sha[11] of the curves in the file curves_K11.m

• helper_funcs.m: this files contains helper functions for all the files in this repo. The descriptions of these functions are given in the file above each function.

• compute_Selmer_11.m: this file contains the main function to compute the Sel_11(E/K) and compute action of Galois on Sel_11(E/K) and output the polynomials h_theta.

Under the current implementation main() in compute_Selmer_11.m takes an elliptic curve with complex multiplication by an order O in which 11 splits and a cyclic quintic extension K of Q having only one prime above 11.