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lgoettgens committed Dec 16, 2024
1 parent 38b9481 commit e1b9d0b
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Original file line number Diff line number Diff line change
Expand Up @@ -6,8 +6,10 @@ Fraction field
of univariate polynomial ring in t over QQ

julia> E = elliptic_curve(Qtf, [0,0,0,0,t^5*(t-1)^2])
Elliptic curve with equation
y^2 = x^3 + t^7 - 2*t^6 + t^5
Elliptic curve
over fraction field of Qt
with equation
y^2 = x^3 + t^7 - 2*t^6 + t^5

julia> j_invariant(E)
0
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Original file line number Diff line number Diff line change
Expand Up @@ -184,8 +184,10 @@ julia> (x,y) = gens(R); P = K_t.([0,0]); # rational point
julia> g, _ = transform_to_weierstrass(g, x, y, P);

julia> E4 = elliptic_curve(g, x, y)
Elliptic curve with equation
y^2 = x^3 + 1//4*t^4*x^2 - 1//2*t^2*x + 1//4
Elliptic curve
over fraction field of univariate polynomial ring
with equation
y^2 = x^3 + 1//4*t^4*x^2 - 1//2*t^2*x + 1//4

julia> g,_ = two_neighbor_step(Y2, fibers_in_Y2[5]);g
t^2*x^3 + (-1//4*t^4 + 2*t)*x^2 + x + y^2
Expand All @@ -197,8 +199,10 @@ julia> (x,y) = gens(R); P = K_t.([0,0]); # rational point
julia> g, _ = transform_to_weierstrass(g, x, y, P);

julia> E5 = elliptic_curve(g, x, y)
Elliptic curve with equation
y^2 = x^3 + (1//4*t^4 - 2*t)*x^2 + t^2*x
Elliptic curve
over fraction field of univariate polynomial ring
with equation
y^2 = x^3 + (1//4*t^4 - 2*t)*x^2 + t^2*x

julia> g,_ = two_neighbor_step(Y2, fibers_in_Y2[6]);g
(t^2 + 2*t + 1)*x^3 + y^2 - 1//4*t^4
Expand All @@ -210,5 +214,7 @@ julia> (x,y) = gens(R); P = K_t.([0,1//2*t^2]); # rational point
julia> g, _ = transform_to_weierstrass(g, x, y, P);

julia> E6 = elliptic_curve(g, x, y)
Elliptic curve with equation
y^2 + (-t^2 - 2*t - 1)//t^4*y = x^3
Elliptic curve
over fraction field of univariate polynomial ring
with equation
y^2 + (-t^2 - 2*t - 1)//t^4*y = x^3

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