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I was studying the following algebraic surface in $\mathbb{P}^5$ defined by the following three quadrics:

\begin{cases} x^2 + xy + y^2=w^2\\ x^2 + 3xz + z^2=t^2\\ y^2 + 5yz + z^2=s^2. \end{cases}

It is a well-known result that its minimal resolution is a K3-surface, which we will denote by X. I am interested in finding out if we know anything about Aut(X). More specifically, if it has any element of infinite order or it is finite. Any help is much appreciated.

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    $\begingroup$ Are you asking about the group of automorphisms defined over C or only those defined over Q ? $\endgroup$
    – Noam D. Elkies
    Commented May 28, 2022 at 18:45
  • $\begingroup$ What is the Picard number of this K3 surface? $\endgroup$
    – Basics
    Commented May 31, 2022 at 13:12
  • $\begingroup$ @NoamD.Elkies over $\bar{\mathbb{Q}}$. But any information about automorphisms over $\mathbb{Q}$ would be useful. $\endgroup$
    – did
    Commented Jun 10, 2022 at 21:57
  • $\begingroup$ @user69559 I don't know. $\endgroup$
    – did
    Commented Jun 10, 2022 at 21:57

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