Index of /~maseap/progs/modularity

 Name                    Last modified       Size  Description

 Parent Directory        14-Jan-2019 06:44      -  Parent
 sieve.m                 05-Oct-2013 18:52    15k  
 gl.m                    05-Oct-2013 18:52     8k  
 Xs3s5.m                 16-Jul-2014 11:17    13k  
 Xs3b5.m                 16-Jul-2014 11:16     9k  
 Xe7.m                   05-Oct-2013 18:52     6k  
 Xd7.m                   05-Oct-2013 18:52     8k  
 Xb5b7.m                 16-Jul-2014 11:10     5k  
 Xb3s5.m                 05-Oct-2013 18:52    15k  
 Xb3b5.m                 05-Oct-2013 18:52     4k  
 Qsqrt5.m                16-Jul-2014 11:22     5k  

This directory contains MAGMA scripts for the verification of the
computations in the paper:

"Elliptic Curves over Real Quadratic Fields are Modular",
by Nuno Freitas, Bao Le Hung, Samir Siksek.

====================================================

gl.m      	For p=3,5,7, determines the odd irreducible subgroups
	  	of GL_2(F_p) having surjective determinant, and whose
		intersection with SL_2(F_p) is absolutely reducible.

====================================================

Xb3b5.m   	Checks the correctness of the model for X(b3,b5)=X_0(15) 
	 	 and j-map X(b3,b5) --> X(1) given by the MAGMA 
	  	"small curves database".

===================================================

Xs3b5.m   	Gives a model for X(s3,b5) and the j-map.

==================================================

Xd7.m     	Derives a model for X(d7) and the j-map, 
		and verifies that they are equivalent to 
		the model and j-map given by Elkies.

==================================================

Xe7.m     	Derives a model for X(e7) and the j-map.

==================================================

Xb5b7.m   	Computations on X(b5,b7)

==================================================

Xb3s5.m   	Computations on X(b3,s5)

=================================================

Xs3s5.m	  	Computations on X(s3,s5)

=================================================

Qsqrt5.m  	Computations for showing that elliptic curves 
		over $\Q(\sqrt{5})$ are modular.

=================================================

sieve.m        A sieve for quadratic points on
	       X(b3,b5,d7)
	       X(s3,b5,d7)
	       X(b3,b5,e7)
               X(s3,b5,e7)