Elliptic curves of rank one over number fields

1. Unbounded rank (or maximal rank) of elliptic curves over Q 
2. Prescribed ranks over number fields beyond rank 1 
3. Silverman’s minimalist conjecture for elliptic fibrations 
4. Generalized Goldfeld’s conjecture for quadratic twist families 
5. Existence of a rank-one curve in quadratic twist families without BSD 
6. PPVW boundedness conjecture for ranks over a fixed number field 

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