Let E be an elliptic curve over a number field K defined by a monic irreducible cubic polynomial F(x). When E is nice at all finite primes of K, we bound its 2-Selmer rank in terms of the 2-rank of a modified ideal class group of the field L = K[x]/(F(x)), which we call the seminarrow class group of L. We then provide several sufficient conditions for E being nice at a finite prime.
|Number of pages||30|
|Journal||Pacific Journal of Mathematics|
|Publication status||Published - 2022|
Bibliographical noteFunding Information:
Yoo was supported by Research Resettlement Fund for the new faculty of Seoul National University. He was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1C1C1007169 and No. 2020R1A5A1016126). Yu was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1C1C1A01007604).
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