$2i$ map of an the elliptic curve over $F_p^2$ defined by $y^2=x^3+x$

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$2i$ map of an the elliptic curve over

$F_p^2$ defined by

$y^2=x^3+x$

isogenies

asked 0 years ago

polynomial
1

I am trying to compute the endomorphism $[2i]$ of the elliptic curve map of The elliptic curve over $F_p^2$ defined by $y^2=x^3+x$ such that [2i] o [2i] = [-4]

but I do not know how. the result should be an isogeny

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answered 0 years ago

yx7
31 ●2 ●1

sage: F = GF(127^2)
sage: E = EllipticCurve(F, [1,0])
sage: i = E.automorphisms()[-1]
sage: assert i^2 == -1
sage: endo = 2 * i
sage: assert endo in End(E)
sage: assert endo^2 == -4
sage: endo
Composite morphism of degree 4 = 1*4:
  From: Elliptic Curve defined by y^2 = x^3 + x over Finite Field in z2 of size 127^2
  To:   Elliptic Curve defined by y^2 = x^3 + x over Finite Field in z2 of size 127^2

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Asked: 0 years ago

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Last updated: Jul 16 '24

2i2i map of an the elliptic curve over F2pF_p^2 defined by y2=x3+xy^2=x^3+x savecancel

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