Hankel-transform Somos-4 conjecture for elliptic-curve division polynomials

Let $E=E(a,b,c,d)$ be the elliptic curve

$$y^2+axy+by=x^3+cx^2+dx,$$

with nonzero discriminant, and let $(0,0)$ be the reference point. Let $h_n$ be the Hankel transform of the sequence generated by

$$g(x)=\frac{2b^4x}{\sqrt{Ax^4+Bx^3+Cx^2+Dx+1}+Fx^2+Gx-1},$$

where $A,B,C,D,F,G$ are the coefficients specified in the paper. Hankel-transform Somos-4 conjecture. The sequence $\frac{h_n}{b^{n^2-2n}}$ is a $(b^2,abd-b^2c+d^2)$ Somos-$4$ sequence which coincides with the division polynomial sequence of $E$. This conjecture connects Hankel transforms and Somos sequences with division polynomials of elliptic curves; the source gives no resolution, so its status remains open.