Sharedsupport / 2014-11-13-ask-size.sagewsOpen in CoCalc
Examples for support purposes...
E = EllipticCurve_from_j(Qp(7,3)(0));
E;
html(table(E.automorphisms(),frame="True").transpose(), hide=0)

show(EllipticCurve_from_j(GF(3,'a')(0)).automorphisms())
Elliptic Curve defined by y^2 = x^3 + (1+O(7^3)) over 7-adic Field with capped relative precision 3
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Generic endomorphism of Abelian group of points on Elliptic Curve defined by y^2 = x^3 + (1+O(7^3)) over 7-adic Field with capped relative precision 3 Via: (u,r,s,t) = (1 + O(7^3), 0, 0, 0) | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Generic endomorphism of Abelian group of points on Elliptic Curve defined by y^2 = x^3 + (1+O(7^3)) over 7-adic Field with capped relative precision 3 Via: (u,r,s,t) = (4 + 2*7 + O(7^3), 0, 0, 0) | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Generic endomorphism of Abelian group of points on Elliptic Curve defined by y^2 = x^3 + (1+O(7^3)) over 7-adic Field with capped relative precision 3 Via: (u,r,s,t) = (5 + 2*7 + O(7^3), 0, 0, 0) | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Generic endomorphism of Abelian group of points on Elliptic Curve defined by y^2 = x^3 + (1+O(7^3)) over 7-adic Field with capped relative precision 3 Via: (u,r,s,t) = (2 + 4*7 + 6*7^2 + O(7^3), 0, 0, 0) | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Generic endomorphism of Abelian group of points on Elliptic Curve defined by y^2 = x^3 + (1+O(7^3)) over 7-adic Field with capped relative precision 3 Via: (u,r,s,t) = (3 + 4*7 + 6*7^2 + O(7^3), 0, 0, 0) | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | Generic endomorphism of Abelian group of points on Elliptic Curve defined by y^2 = x^3 + (1+O(7^3)) over 7-adic Field with capped relative precision 3 Via: (u,r,s,t) = (6 + 6*7 + 6*7^2 + O(7^3), 0, 0, 0) | +----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
[Generic endomorphism of Abelian group of points on Elliptic Curve defined by y^2 = x^3 + x over Finite Field of size 3  Via:  (u,r,s,t) = (1, 0, 0, 0),Generic endomorphism of Abelian group of points on Elliptic Curve defined by y^2 = x^3 + x over Finite Field of size 3  Via:  (u,r,s,t) = (2, 0, 0, 0)]\left[\begin{array}{l} \text{\texttt{Generic{ }endomorphism{ }of{ }Abelian{ }group{ }of{ }points{ }on{ }Elliptic{ }Curve{ }defined{ }by{ }y{\char`\^}2{ }={ }x{\char`\^}3{ }+{ }x{ }over{ }Finite{ }Field{ }of{ }size{ }3}}\\ \text{\texttt{{ }{ }Via:{ }{ }(u,r,s,t){ }={ }(1,{ }0,{ }0,{ }0)}} \end{array}, \begin{array}{l} \text{\texttt{Generic{ }endomorphism{ }of{ }Abelian{ }group{ }of{ }points{ }on{ }Elliptic{ }Curve{ }defined{ }by{ }y{\char`\^}2{ }={ }x{\char`\^}3{ }+{ }x{ }over{ }Finite{ }Field{ }of{ }size{ }3}}\\ \text{\texttt{{ }{ }Via:{ }{ }(u,r,s,t){ }={ }(2,{ }0,{ }0,{ }0)}} \end{array}\right]