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- W4313531132 abstract "Rizzo showed that the family of elliptic curves W(t):y2=x3+tx2−(t+3)x+1, a well-known example of Washington, has root number W(W(t))=−1 for all t∈Z [11]. In this paper we generalise this example and identify the families of small degree on which this phenomenon happens. Motivated by results from [2] and [5], we study in detail the two families Fs(t):y2=x3+3tx2+3sx+st and Lw,s,v(t):wy2=x3+3(t2+v)x2+3sx+s(t2+v) and describe necessary and sufficient conditions for which subfamilies of Fs(t) have constant root number on integer fibres. We further prove similar but partial results on Lw,s,v(t). Our results give examples of subfamilies for which there is rank elevation at integer fibres." @default.
- W4313531132 created "2023-01-06" @default.
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- W4313531132 date "2023-05-01" @default.
- W4313531132 modified "2023-09-28" @default.
- W4313531132 title "Constant root number on integer fibres of elliptic surfaces" @default.
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- W4313531132 doi "https://doi.org/10.1016/j.jnt.2022.11.006" @default.
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