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Hello all,

I tried the following on sagecell online

K.<z2> = NumberField(x^2+1)

E = EllipticCurve(K, [3,105/16])

P = E.point((7,-77/4))

E.height_pairing_matrix([P,P])

and I get the out put

[2.13279604624597 2.82594322680591]

[2.82594322680591 2.13279604624597]

Shouldn't all the coefficients in output matrix be the same given that P and P are linearly dependent?

Thank you in advance!

Hello all,

I tried the following on sagecell online

K.<z2> = NumberField(x^2+1)
NumberField(x^2+1)
  
E = EllipticCurve(K, [3,105/16])[3,105/16])
  
P = E.point((7,-77/4))E.point((7,-77/4))
  
E.height_pairing_matrix([P,P])E.height_pairing_matrix([P,P])

[2.13279604624597 2.82594322680591]
2.82594322680591]
  
[2.82594322680591 2.13279604624597]2.13279604624597]

Hello all,

I tried the following on sagecell online

K.<z2> = NumberField(x^2+1)

E = EllipticCurve(K, [3,105/16])

P = E.point((7,-77/4))

E.height_pairing_matrix([P,P])

and I get the out put

[2.13279604624597 2.82594322680591]

[2.82594322680591 2.13279604624597]

Shouldn't all the coefficients in output matrix be the same given that P and P are linearly dependent?

Thank you in advance!