Geodesic
Counting points on hyperelliptic curves of type $y^2=x^{2g+1}+ax^{g+1}+bx$
Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 30-33

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In this work, we investigate hyperelliptic curves of type shown in the title over the finite field $\mathbb F_q$, $q=p^n$, $p>2$. For the case of $g=3$ or $4$, $p\nmid4g$ and $b$ is a $4g$-root, we provide efficient methods to compute the number of points in the Jacobian of the curve.
Keywords: hyperelliptic curves, point counting.
Mots-clés : Cartier–Manin matrix, Legendre polynomials 
@article{PDMA_2018_11_a8,
     author = {S. A. Novoselov},
     title = {Counting points on hyperelliptic curves of type $y^2=x^{2g+1}+ax^{g+1}+bx$},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {30--33},
     publisher = {mathdoc},
     number = {11},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2018_11_a8/}
}
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S. A. Novoselov. Counting points on hyperelliptic curves of type $y^2=x^{2g+1}+ax^{g+1}+bx$. Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 30-33. http://geodesic.mathdoc.fr/item/PDMA_2018_11_a8/