On the Equation $Y^2 = X^5 + k$
Bremner, Andrew
Experiment. Math., Tome 17 (2008) no. 1, p. 371-374 / Harvested from Project Euclid
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We show that there are infinitely many nonisomorphic curves $Y^2 = X^5 + k$, $k \in {\mathbb Z}$}, possessing at least twelve finite points $k>0$, and at least six finite points for $k<$. We also determine all rational points on the curve $Y^2=X^5-7$.
Publié le : 2008-05-15
Classification:  Fifth powers,  genus two curve,  elliptic curve,  11D41,  11D25,  11G05,  11G30 
@article{1227121389,
     author = {Bremner, Andrew},
     title = {On the Equation $Y^2 = X^5 + k$},
     journal = {Experiment. Math.},
     volume = {17},
     number = {1},
     year = {2008},
     pages = { 371-374},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1227121389}
}

Bremner, Andrew. On the Equation $Y^2 = X^5 + k$. Experiment. Math., Tome 17 (2008) no. 1, pp.  371-374. http://gdmltest.u-ga.fr/item/1227121389/