compute the equation for elliptic curves from lattices
 
  
 
  
 
 
 
 
 
 
    
        
        asked 3 years ago  
 
 Lee gravatar image  
 
 
 
 
    
        
        updated 3 years ago  
 
 
 
 
 
Given a lattice in C, is there commands in Sage or Pari to compute the equation of the elliptic curves associated to the lattice? or in other words, compute c4 and c6 of the lattice?
 
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1
How exactly the lattice is given? Please provide an example.
Max Alekseyev gravatar imageMax Alekseyev (
    
        3 years ago
    )
For example, given a basis
[1.4752770112052821796 - 0.6182637476411826238*i,
 1.6774834051116878106 - 2.205022990784728253*i,]
of the lattice. How can I compute the equation of C/Λ?
Lee gravatar imageLee (
    
        3 years ago
    )
You'd need to compute Eisenstein series as explained at https://math.stackexchange.com/q/1291245
Max Alekseyev gravatar imageMax Alekseyev (
    
        3 years ago
    )
Thanks a lot for the anwser ! So there is no program or command in Sage or Pari to do that directly, right?
Lee gravatar imageLee (
    
        3 years ago
    )
There is no single command for that, but related functionality is present in Sage and Pari -- e.g., see answers at https://ask.sagemath.org/question/51409/
Max Alekseyev gravatar imageMax Alekseyev (
    
        3 years ago
    )

            
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