@@ -1426,7 +1426,7 @@ def twists(self):
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In characteristic 3, the number of twists is 2 except for
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`j=0=1728`, when there are either 4 or 6 depending on whether the
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- field has odd or even degree over `\FF_3 `::
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+ field has odd or even degree over `\GF{3} `::
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sage: K = GF(3**5)
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sage: [E.ainvs() for E in EllipticCurve(j=K(1)).twists()]
@@ -1454,7 +1454,7 @@ def twists(self):
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In characteristic 2, the number of twists is 2 except for
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`j=0=1728`, when there are either 3 or 7 depending on whether the
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- field has odd or even degree over `\FF_2 `::
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+ field has odd or even degree over `\GF{2} `::
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sage: K = GF(2**7)
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sage: [E.ainvs() for E in EllipticCurve(j=K(1)).twists()]
@@ -1553,7 +1553,7 @@ def curves_with_j_0(K):
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Examples:
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- For `K=\FF_q ` where `q\equiv1\mod{6}` there are six curves, the sextic twists of `y^2=x^3+1`::
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+ For `K=\GF{q} ` where `q\equiv1\mod{6}` there are six curves, the sextic twists of `y^2=x^3+1`::
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sage: from sage.schemes.elliptic_curves.ell_finite_field import curves_with_j_0
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sage: sorted(curves_with_j_0(GF(7)), key = lambda E: E.a_invariants())
@@ -1571,7 +1571,7 @@ def curves_with_j_0(K):
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Elliptic Curve defined by y^2 = x^3 + (2*z2+2) over Finite Field in z2 of size 5^2,
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Elliptic Curve defined by y^2 = x^3 + (4*z2+1) over Finite Field in z2 of size 5^2]
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- For `K=\FF_q ` where `q\equiv5\mod{6}` there are two curves,
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+ For `K=\GF{q} ` where `q\equiv5\mod{6}` there are two curves,
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quadratic twists of each other by `-3`: `y^2=x^3+1` and
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`y^2=x^3-27`::
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@@ -1614,7 +1614,7 @@ def curves_with_j_1728(K):
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Examples:
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- For `K=\FF_q ` where `q\equiv1\mod{4} there are four curves, the quartic twists of `y^2=x^3+x`::
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+ For `K=\GF{q} ` where `q\equiv1\mod{4} there are four curves, the quartic twists of `y^2=x^3+x`::
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sage: from sage.schemes.elliptic_curves.ell_finite_field import curves_with_j_1728
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sage: sorted(curves_with_j_1728(GF(5)), key = lambda E: E.a_invariants())
@@ -1628,7 +1628,7 @@ def curves_with_j_1728(K):
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Elliptic Curve defined by y^2 = x^3 + (z2+4)*x over Finite Field in z2 of size 7^2,
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Elliptic Curve defined by y^2 = x^3 + (5*z2+4)*x over Finite Field in z2 of size 7^2]
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- For `K=\FF_q ` where `q\equiv3\mod{4} there are two curves,
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+ For `K=\GF{q} ` where `q\equiv3\mod{4} there are two curves,
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quadratic twists of each other by `-1`: `y^2=x^3+x` and
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`y^2=x^3-x`::
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@@ -1664,12 +1664,12 @@ def curves_with_j_0_char2(K):
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.. NOTE::
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The number of twists is either 3 or 7 depending on whether
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- the field has odd or even degree over `\FF_2 `. See
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+ the field has odd or even degree over `\GF{2} `. See
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[Connell1999]_, pages 429-431.
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Examples:
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- In odd degree, there are three isomorphism classes all with representatives defined over `\FF_2 `::
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+ In odd degree, there are three isomorphism classes all with representatives defined over `\GF{2} `::
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sage: from sage.schemes.elliptic_curves.ell_finite_field import curves_with_j_0_char2
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sage: K = GF(2**7)
@@ -1751,7 +1751,7 @@ def curves_with_j_0_char3(K):
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.. NOTE::
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The number of twists is either 4 or 6 depending on whether
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- the field has odd or even degree over `\FF_3 `. See
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+ the field has odd or even degree over `\GF{3} `. See
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[Connell1999]_, pages 429-431.
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Examples:
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