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Elliptic curve

Index Mathematics Fields of mathematics Fields of abstract algebra Group theory
 1 By others on same topic  0 Discussions  1970-01-01  See my version

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 Articles by others on the same topic (1)

Elliptic curve by Ciro Santilli 37  Updated 2025-05-29  +Created 1970-01-01
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An elliptic curve is defined by numbers a and b. The curve is the set of all points (x,y) of the real plane that satisfy the Equation 1. "Definition of the elliptic curves"
y2=x3+ax+b
(1)
Equation 1.
Definition of the elliptic curves
.
Figure 1.
Plots of real elliptic curves for various values of a and b
. Source.
Equation 1. "Definition of the elliptic curves" definies elliptic curves over any field, it doesn't have to the real numbers. Notably, the definition also works for finite fields, leading to elliptic curve over a finite fields, which are the ones used in Elliptic-curve Diffie-Hellman cyprotgraphy.
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