elliptic curve

mathematics

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July 23, 2026

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An elliptic curve is a type of cubic curve, or algebraic curve of order 3, confined to a region known as a torus. In mathematics, the Birch and Swinnerton-Dyer conjecture relates the number of rational points on an elliptic curve to the value of an associated function. If this function equals zero, the curve has an infinite number of rational points; if it's not zero, the curve has a finite number of rational points. This conjecture is one of the seven Millennium Problems, with a $1 million prize for its solution. Algebraic geometry, a field that studies solutions to polynomial equations, is where elliptic curves are often analyzed.12

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Birch and Swinnerton-Dyer conjecture
…mathematics, the conjecture that an elliptic curve (a type of cubic curve, or algebraic curve of order 3, confined to a region known as a torus) has either an infinite number of rational points (solutions) or a finite number of rational points, according to whether an associated function is equal…
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…mathematics, the conjecture that an elliptic curve (a type of cubic curve, or algebraic curve of order 3, confined to a region known as a torus) has either an infinite number of rational points (solutions) or a finite number of rational points, according to whether an associated function is equal…
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John Tate
…of his particular interests was elliptic curves, which are real number solutions to cubic polynomial equations, such as y² − x³ = c. This work has applications in the field of cryptography in that it can be used to factor extremely large prime numbers, which are used in secure communications.
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…of his particular interests was elliptic curves, which are real number solutions to cubic polynomial equations, such as y² − x³ = c. This work has applications in the field of cryptography in that it can be used to factor extremely large prime numbers, which are used in secure communications.
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