Dataset of congruent number elliptic curves: 2-Selmer rank, 3-Selmer rank, MW rank, analytic rank, BSD parameters and Frobenius traces

This is the dataset for the paper Unveiling Arithmetic Statistics of Congruent Numbers via Data Science and Machine Learning by Priyavrat Deshpande, Aditya Karnataki and Pratiksha Shingavekar. three_mil_2selmer.parquet - this file contains 2-Selmer ranks of congruent number elliptic curves corresponding to square-free numbers up to 3 million. The first column labeled 'n' contains these square-free numbers; the equation of the curve E_n is y^2 = x^3 - n^2x. Hence, only 'n' is needed to uniquely identify the curve. Second column contains the 2-Selmer rank, computed using Sage. Third column contains residue of n modulo 8. frobenius_cn1k.parquet - this file contains Frobenius traces of congruent number elliptic curves. The first column is the curve identifier 'n'. The second column "iscongruent' is 1 if n is congruent otherwise it is 0. Later 1000 columns correspond to first 1000 primes each entry is the Frobenius trace a_p of E_n. cn_with_2selmer_1mil.csv - For congruent number curves corresponding to square-free numbers till 1 million, the file contains MW rank, regulator, 2-Selmer rank, analytic order of Sha and the conductor. bsd_sqf1mil.csv - The file contains regulator, torsion order, real period and special value of congruent number curves. All these parameters appear in the BSD formula. an_rk.csv - Analytic rank of congruent number curves threeselmer.csv - 3-Selmer ranks of congruent number curves cn_prediction_selmerinfo.csv - data used for predicting congruent numbers using Selmer ranks and the valuation of the modular degree. mwranks_3mil.csv - it contains square-free numbers up to 3 million and MW ranks of the corresponding congruent number curves.