{"title":"关于三次数域上椭圆曲线的循环扭转(II)","authors":"Jian Wang","doi":"10.5802/jtnb.1100","DOIUrl":null,"url":null,"abstract":"This is the third part of a series of papers discussing the cyclic torsion subgroup of elliptic curves over cubic number fields. For $N=39$, we show that $\\mathbb{Z}/N\\mathbb{Z}$ is not a subgroup of $E(K)_{tor}$ for any elliptic curve $E$ over a cubic number field $K$.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On the cyclic torsion of elliptic curves over cubic number fields (II)\",\"authors\":\"Jian Wang\",\"doi\":\"10.5802/jtnb.1100\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This is the third part of a series of papers discussing the cyclic torsion subgroup of elliptic curves over cubic number fields. For $N=39$, we show that $\\\\mathbb{Z}/N\\\\mathbb{Z}$ is not a subgroup of $E(K)_{tor}$ for any elliptic curve $E$ over a cubic number field $K$.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-05-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5802/jtnb.1100\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/jtnb.1100","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the cyclic torsion of elliptic curves over cubic number fields (II)
This is the third part of a series of papers discussing the cyclic torsion subgroup of elliptic curves over cubic number fields. For $N=39$, we show that $\mathbb{Z}/N\mathbb{Z}$ is not a subgroup of $E(K)_{tor}$ for any elliptic curve $E$ over a cubic number field $K$.
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