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This is a Quantitative Study study.

The distribution of ℓ∞-Selmer groups in degree ℓ twist families I

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The technique shows that 100% of quadratic twists of elliptic curves exhibit rank at most 1, which is significant for understanding their distribution.
We delve into the distribution of ℓ^{∞}-Selmer groups, establishing relationships with Cohen–Lenstra–Gerth heuristics in Galois module families.
Developing the theory of fixed point Selmer groups provides a foundational approach to studying ℓ^{∞}-Selmer groups in the paper.
This work sets the stage for further analysis and control of fixed point Selmer groups in the upcoming sequel.

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This paper reveals the distribution of Selmer groups in elliptic curves over number fields, indicating 100% have rank at most 1.

Alexander Smith (2025) studied this question.

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