We show that if E is an elliptic curve over Q with a Q-rational isogeny of degree 7, then the image of the 7-adic Galois representation attached to E is as large as allowed by the isogeny, except for ...

Elliptic curves — actually plane curves that are very different from ellipses — have been used in key realms of number theory, such as the proof of Fermat's last theorem. In the mid-1980s, ...

By extending the scope of a key insight behind Fermat’s Last Theorem, four mathematicians have made great strides toward ...

Operations on elliptic curves The security of ECC depends on the difficulty of the Elliptic Curve Discrete Logarithm Problem. This problem is defined as follows: let and be two points on an elliptic ...

As numbers go, 1729, the Hardy-Ramanujan number, is not new to math enthusiasts. But now, this number has triggered a major discovery — on Ramanujan and the theory of what are known as ...

JULIÁN AGUIRRE, ANDREJ DUJELLA, JUAN CARLOS PERAL, ON THE RANK OF ELLIPTIC CURVES COMING FROM RATIONAL DIOPHANTINE TRIPLES, The Rocky Mountain Journal of Mathematics, Vol. 42, No. 6 (2012), pp.

Elliptic curves may sound esoteric, but they are part of our day-to-day lives. They are used in cryptography -- the creation of codes that are difficult to break.

Elliptic curve cryptography (ECC) uses points on an elliptic curve to derive a 163-bit public key that is equivalent in strength to a 1024-bit RSA key.