  Let $G$ be a simple graph with vertex set $V(G) = \{v_1, v_2,\ldots, v_n\}$.
The elliptic Sombor matrix of $G$, denoted by $A_{ESO}(G)$, is defined as the
$n\times n$ matrix whose $(i,j)$-entry is $(d_i+d_j)\sqrt{d_i^2+d_j^2}$ if
$v_i$ and $v_j$ are adjacent and $0$ for another cases. Let the eigenvalues of
the elliptic Sombor matrix $A_{ESO}(G)$ be $\rho_1\geq \rho_2\geq \ldots\geq
\rho_n$ which are the roots of the elliptic Sombor characteristic polynomial
$\prod_{i=1}^n (\rho-\rho_i)$. The elliptic Sombor energy ${E_{ESO}}$ of $G$ is
the sum of absolute values of the eigenvalues of $A_{ESO}(G)$. In this paper,
we compute the elliptic Sombor characteristic polynomial and the elliptic
Sombor energy for some graph classes. We compute the elliptic Sombor energy of
cubic graphs of order $10$ and as a consequence, we see that two $k$-regular
graphs of the same order may have different elliptic Sombor energy.
