Determinantal representation, elliptic curves, Weierstrass $\wp$-functions, Riemann theta functions.
Helton and Vinnikov proved that every hyperbolic ternary form admits a symmetric derminantal representation via Riemann theta functions. In the case the algebraic curve of the hyperbolic ternary form is elliptic, the determinantal representation of the ternary form is formulated by using Weierstrass $\wp$-functions in place of Riemann theta functions. An example of this approach is given.
Chien, Mao-Ting and Nakazato, Hiroshi.
"Determinantal representations of elliptic curves via Weierstrass elliptic functions",
Electronic Journal of Linear Algebra,
Volume 34, pp. 125-136.
DOI: https://doi.org/10.13001/1081-3810, 1537-9582.3609