Adventures-in-Supersingularland-Data

Data and code associated with the article Adventures in Supersingularland.

Authors: Sarah Arpin, Catalina Camacho-Navarro, Kristin Lauter, Joelle Lim, Kristina Nelson, Travis Scholl, Jana Sotáková.

Contents

Data

When Are Conjugates 2-Isogenous.csv Lists the number of conjugate pairs that are 2-isogenous for primes 5 to 100193.

When Are Conjugates 3-Isogenous.csv Lists the number of conjugate pairs that are 3-isogenous for primes 5 to 100193.

Attachment.csv Lists whether or not attachment occured for primes between 50,000 and 100,000. Generated by the code in Attachment.py.

Distances Between Random Pairs and Components 1 mod 4.csv Lists the distance between 100 random pairs of vertices, as well as the average distance between all components of the Fp subgraph for some primes between 10,000 and 66,000. All primes were congruent to 1 mod 4.

Pairs Through Fp Random Sampling.csv For primes between 50,000 and 100,000, a random subset of 1000 vertex pairs were tested. Lists number of these vertex pairs with a shortest path through Fp and the number of vertices with a path through Fp to their conjugate.

Pairs Through Fp Small.csv For primes between 1000 and 5000, lists the number of times a vertex in the graph had a shortest path to its conjugate passing through Fp, the total number of conjugate pairs, the number of times a pair of vertices in the graph had a shortest path passing through Fp, and the total number of vertex pairs.

Pairs Through a Random Subgraph.csv For primes between 1000 and 5000, lists the number of times a vertex in the graph had a shortest path to its conjugate passing through one of 10 random subgraphs. Also Lists the total number of conjugate pairs, the number of times a pair of vertices in the graph had a shortest path passing through the random subgraphs, and the total number of vertex pairs.

Code

Walk.sage Contains the isogeny-graph generating function.

Attachment.py Contains the script used to test whether attachment occured for primes between 50,000 and 100,000.

Paths_Through_Fp_and_Distances.py Contains the functions and script used to compute data about when the shortest path between vertices went through the Fp subgraph, as well as the distances between random components. Output stored in Pairs Through a Random Subgraph.csv, Pairs Through Fp Small.csv, Pairs Through Fp Random Sampling.csv and Distances Between Random Pairs and Components 1 mod 4.csv.