ellisotree

Function: ellisotree
Section: elliptic_curves
C-Name: ellisotree
Prototype: G
Help: ellisotree(E): E being an elliptic curve over Q or a set of isogenous
 rational curves as given by ellisomat, return minimal models of the isomorphism
 classes of elliptic curves isogenous to E (or in the set) and the oriented
 graph of isogenies of prime degree (adjacency matrix).
Doc: Given an elliptic curve $E$ defined over $\Q$ or a set of
 $\Q$-isogenous curves as given by \kbd{ellisomat}, return a pair $[L,M]$ where

 \item $L$ lists the minimal models of the isomorphism classes of elliptic
 curves $\Q$-isogenous to $E$ (or in the set of isogenous curves),

 \item $M$ is the adjacency matrix of the prime degree isogenies tree:
 there is an edge from $E_i$ to $E_j$ if there is an isogeny $E_i \to E_j$ of
 prime degree such that the N\'eron differential forms are preserved.

 \bprog
 ? E = ellinit("14a1");
 ? [L,M] = ellisotree(E);
 ? M
 %3 =
 [0 0 3 2 0 0]

 [3 0 0 0 2 0]

 [0 0 0 0 0 2]

 [0 0 0 0 0 3]

 [0 0 0 3 0 0]

 [0 0 0 0 0 0]
 ? [L2,M2] = ellisotree(ellisomat(E,2,1));
 %4 =
 [0 2]

 [0 0]
 ? [L3,M3] = ellisotree(ellisomat(E,3,1));
 ? M3
 %6 =
 [0 0 3]

 [3 0 0]

 [0 0 0]
 @eprog\noindent Compare with the result of \kbd{ellisomat}.
 \bprog
 ? [L,M]=ellisomat(E,,1);
 ? M
 %7 =
 [1  3  3 2  6  6]

 [3  1  9 6  2 18]

 [3  9  1 6 18  2]

 [2  6  6 1  3  3]

 [6  2 18 3  1  9]

 [6 18  2 3  9  1]
 @eprog