Geodesic
Characteristic polynomials of the curve $y^2=x^7+ax^4+bx$ over finite fields
Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 44-46

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In this work, we list all possible characteristic polynomials of the Frobenius endomorphism for genus $3$ hyperelliptic curves of type $y^2 = x^7 + a x^4 + b x$ over finite field $\mathbb{F}_q$ of characteristic $p>3$.
Keywords: hyperelliptic curves, characteristic polynomials, point-counting
Mots-clés : genus $3$. 
@article{PDMA_2019_12_a11,
     author = {S. A. Novoselov and Y. F. Boltnev},
     title = {Characteristic polynomials of the curve $y^2=x^7+ax^4+bx$ over finite fields},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {44--46},
     publisher = {mathdoc},
     number = {12},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2019_12_a11/}
}
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S. A. Novoselov; Y. F. Boltnev. Characteristic polynomials of the curve $y^2=x^7+ax^4+bx$ over finite fields. Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 44-46. http://geodesic.mathdoc.fr/item/PDMA_2019_12_a11/