{"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":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":" ","pages":""},"PeriodicalIF":0.3000,"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\":48896,\"journal\":{\"name\":\"Journal De Theorie Des Nombres De Bordeaux\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2020-05-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal De Theorie Des Nombres De Bordeaux\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5802/jtnb.1100\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal De Theorie Des Nombres De Bordeaux","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/jtnb.1100","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","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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