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This example should be the elliptic curve with j-invariant 0 and can be found in Deligne's paper Preuve des conjectures de Tate et de Shafarevitch (p. 29). If you are more interested in small values for elliptic curves, the article On the essential minimum of Faltings' height by Burgos Gil, Menares and Rivera-Letelier may be interesting for you. An example of negative value in genus 2 can be found in Sur le calcul explicitedes “classes de Chern” des surfaces arithmétiques de genre 2 by Bost, Mestre and Moret-Bailly.

This example should be the elliptic curve with j-invariant 0 and can be found in Deligne's paper Preuve des conjectures de Tate et de Shafarevitch (p. 29). If you are more interested in small values for elliptic curves, the article On the essential minimum of Faltings' height by Gil, Menares and Rivera-Letelier may be interesting for you. An example of negative value in genus 2 can be found in Sur le calcul explicitedes “classes de Chern” des surfaces arithmétiques de genre 2 by Bost, Mestre and Moret-Bailly.

This example should be the elliptic curve with j-invariant 0 and can be found in Deligne's paper Preuve des conjectures de Tate et de Shafarevitch (p. 29). If you are more interested in small values for elliptic curves, the article On the essential minimum of Faltings' height by Burgos Gil, Menares and Rivera-Letelier may be interesting for you. An example of negative value in genus 2 can be found in Sur le calcul explicitedes “classes de Chern” des surfaces arithmétiques de genre 2 by Bost, Mestre and Moret-Bailly.

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This example should be the elliptic curve with j-invariant 0 and can be found in Deligne's paper Preuve des conjectures de Tate et de Shafarevitch (p. 29). If you are more interested in small values for elliptic curves, the article On the essential minimum of Faltings' height by Gil, Menares and Rivera-Letelier may be interesting for you. An example of an negative value in genus 2 can be found in Sur le calcul explicitedes “classes de Chern” des surfaces arithmétiques de genre 2 by Bost, Mestre and Moret-Bailly.

This example should be the elliptic curve with j-invariant 0 and can be found in Deligne's paper Preuve des conjectures de Tate et de Shafarevitch (p. 29). If you are more interested in small values for elliptic curves, the article On the essential minimum of Faltings' height by Gil, Menares and Rivera-Letelier may be interesting for you. An example of an negative value in genus 2 can be found in Sur le calcul explicitedes “classes de Chern” des surfaces arithmétiques de genre 2 by Bost, Mestre and Moret-Bailly.

This example should be the elliptic curve with j-invariant 0 and can be found in Deligne's paper Preuve des conjectures de Tate et de Shafarevitch (p. 29). If you are more interested in small values for elliptic curves, the article On the essential minimum of Faltings' height by Gil, Menares and Rivera-Letelier may be interesting for you. An example of negative value in genus 2 can be found in Sur le calcul explicitedes “classes de Chern” des surfaces arithmétiques de genre 2 by Bost, Mestre and Moret-Bailly.

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This example should be the elliptic curve with j-invariant 0 and can be found in Deligne's paper Preuve des conjectures de Tate et de Shafarevitch (p. 29). If you are more interested in small values for elliptic curves, the article On the essential minimum of Faltings' height by Gil, Menares and Rivera-Letelier may be interesting for you. An example of an negative value in genus 2 can be found in Sur le calcul explicitedes “classes de Chern” des surfaces arithmétiques de genre 2 by Bost, Mestre and Moret-Bailly.