# What is the modular form of an elliptic curve?

## What is the modular form of an elliptic curve?

A modular elliptic curve is an elliptic curve E that admits a parametrisation X0(N) → E by a modular curve. This is not the same as a modular curve that happens to be an elliptic curve, something that could be called an elliptic modular curve.

### Is Fermat last theorem true?

(b) Because there cannot be a contradiction, it also proves that the kinds of elliptic curves described by Frey cannot actually exist. Therefore no solutions to Fermat’s equation can exist either, so Fermat’s Last Theorem is also true.

What does it mean for a curve to be modular?

From Wikipedia, the free encyclopedia. In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular group of integral 2×2 matrices SL(2, Z).

What is Fermat’s theorem in cryptography?

Fermat’s little theorem states that if p is a prime number, then for any integer a, the number a p – a is an integer multiple of p. ap ≡ a (mod p).

## Who first proved Fermat’s last theorem?

Although some general results on Fermat’s Last Theorem were published in the early 19th century by Niels Henrik Abel and Peter Barlow, the first significant work on the general theorem was done by Sophie Germain.

### Who first proved Fermat’s Last Theorem?

Why is Fermat’s Last Theorem important?

actually proved was far deeper and more mathematically interesting than its famous corollary, Fermat’s last theorem, which demonstrates that in many cases the value of a mathematical problem is best measured by the depth and breadth of the tools that are developed to solve it.

What is elliptic curve theory?

Elliptic curves are curves defined by a certain type of cubic equation in two variables. The set of rational solutions to this equation has an extremely interesting structure, including a group law. The theory of elliptic curves was essential in Andrew Wiles’ proof of Fermat’s last theorem.

## How does ECC cryptography work?

How does elliptic curve cryptography work? # Based on the values given to a and b, this will determine the shape of the curve. Elliptical curve cryptography uses these curves over finite fields to create a secret that only the private key holder is able to unlock.