to 2g + 1, the curve is called an imaginary hyperelliptic curve. Meanwhile, a curve of degree 2g + 2 is termed a real hyperelliptic curve. This statement...

hyperelliptic curve. The computations differ depending on the number of points at infinity. Imaginary hyperelliptic curves are hyperelliptic curves with...

just as we use the group of points on an elliptic curve in ECC. An (imaginary) hyperelliptic curve of genus g {\displaystyle g} over a field K {\displaystyle...

there are two types of hyperelliptic curves, a class of algebraic curves: real hyperelliptic curves and imaginary hyperelliptic curves which differ by the...

(an abelian surface): what would now be called the Jacobian of a hyperelliptic curve of genus 2. After Abel and Jacobi, some of the most important contributors...

- includes examples Explicit calculation of period matrices for hyperelliptic curves - includes examples Algorithm for computing periods of hypersurfaces...

genus 2 curve C / F 41 : y 2 + y = x 5 , {\displaystyle C/{\bf {F}}_{41}:y^{2}+y=x^{5},} which was introduced in the section on hyperelliptic curves. The...

surfaces have Riemann surface structures, as (compactifications of) hyperelliptic surfaces y2 = Q(x), where Q is a complex polynomial of degree 2g + 1...

609–631. MR1879675 S. Paulus, H.-G. Rück: Real and imaginary quadratic representations of hyperelliptic function fields. (English summary) Math. Comp. 68...

in degrees and denoted by the Greek letter lambda (λ). Meridians are imaginary semicircular lines running from pole to pole that connect points with...