Cone/Two-dimensional/Edges/Signature/Exercise

We consider the twodimensional cone ${}C$ given by the edges ${}\mathbb {R} _{\geq 0}{\begin{pmatrix}7\\2\end{pmatrix}}$ and ${}\mathbb {R} _{\geq 0}{\begin{pmatrix}5\\6\end{pmatrix}}$ and the corresponding monoid ${}C\cap \mathbb {Z} ^{2}$. Determine the describing integral linear forms and the signatures of the cone.

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