2020-05-29 05:14:15 +0200 received badge ● Notable Question (source) 2020-01-09 12:10:56 +0200 received badge ● Popular Question (source) 2019-03-01 18:20:10 +0200 received badge ● Student (source) 2019-02-22 13:57:41 +0200 commented answer Elliptic Curve Twist Should it not the resulted Elliptic Curve be defined over $F_{p^{2}}$ instead of $F_{p^{8}}$ 2019-02-22 00:46:32 +0200 asked a question Elliptic Curve Twist Hello, I am trying to compute the quadratic twist for an example of an Elliptic curve defined over a GF(p^8) Field: With p=3351951982486667453837338848452726606028033606935065896469552348842908133596080151967071453287452469772970937967942438575522391344438242727636910570385409 and an Elliptic curve defined as: E = ElllipticCurve(GF(p),[1,0])  given the extensions: F2. = GF(p^2, modulus=x^2 + 11) F4. = GF(p^4, modulus=x^4 + 11) F8. = GF(p^8, modulus=x^8 + 11)  I am trying to compute a twist of the elliptic curve defined over F8, of the twist equation form: y^2=x^3+a w^4 x, while a=1, and w satisfies the following: $w\in F_{p^8}$ and $w^4 \in F_{p^2}$, $w^2 \in F_{p^4}$ and $w^3 \in F_{p^{8}} \setminus F_{p^{4}}$ Is there any sage command that would help with this problem ? Another way but I didn't know how to write it in sage: {1,w,w^2,w^3} are the basis of $F_{p^8}$ as a vector space over $F_{p^{2}}$. Thanks in advance.