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Ben C
Ben C
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Is it known if the Selmer ranks of quadratic twist families are unbounded?

Suppose that $E/K$ is an elliptic curve defined over a number field. For each quadratic extension $F/K$ I can form the twist $E^F$ via the character of $F$. Is there a choice of $E/K$ such that the Selmer ranks $\mathrm{rank} Sel_n(E^F)$$\mathrm{rank} \, \mathrm{Sel}_n(E^F)$ are known to be unbounded?

Is it known if the Selmer ranks of quadratic twist families are unbounded?

Suppose that $E/K$ is an elliptic curve defined over a number field. For each quadratic extension $F/K$ I can form the twist $E^F$ via the character of $F$. Is there a choice of $E/K$ such that the Selmer ranks $\mathrm{rank} Sel_n(E^F)$ are known to be unbounded?

Is it known if the Selmer ranks of quadratic twist families are unbounded?

Suppose that $E/K$ is an elliptic curve defined over a number field. For each quadratic extension $F/K$ I can form the twist $E^F$ via the character of $F$. Is there a choice of $E/K$ such that the Selmer ranks $\mathrm{rank} \, \mathrm{Sel}_n(E^F)$ are known to be unbounded?

Source Link
Ben C
Ben C
  • 3.7k
  • 7
  • 25

Selmer ranks unbounded?

Is it known if the Selmer ranks of quadratic twist families are unbounded?

Suppose that $E/K$ is an elliptic curve defined over a number field. For each quadratic extension $F/K$ I can form the twist $E^F$ via the character of $F$. Is there a choice of $E/K$ such that the Selmer ranks $\mathrm{rank} Sel_n(E^F)$ are known to be unbounded?