Geodesic
Optimal curves differing by a 3-isogeny
Dongho Byeon 1   ; Donggeon Yhee 1
1 Department of Mathematics Seoul National University Seoul, Korea
Acta Arithmetica, Tome 158 (2013) no. 3, pp. 219-227 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Stein and Watkins conjectured that for a certain family of elliptic curves $E$, the $X_0(N)$-optimal curve and the $X_1(N)$-optimal curve of the isogeny class $\mathcal {C}$ containing $E$ of conductor $N$ differ by a 3-isogeny. In this paper, we show that this conjecture is true.
DOI : 10.4064/aa158-3-2
Keywords: stein watkins conjectured certain family elliptic curves optimal curve optimal curve isogeny class mathcal containing conductor differ isogeny paper conjecture

Dongho Byeon  1   ; Donggeon Yhee  1

1 Department of Mathematics Seoul National University Seoul, Korea 
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Dongho Byeon; Donggeon Yhee. Optimal curves differing by a 3-isogeny. Acta Arithmetica, Tome 158 (2013) no. 3, pp. 219-227. doi: 10.4064/aa158-3-2

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