3 ms·
> even elliptic curves with no rational points on them still have points in finite fields That’s interesting. How is that possible?
by empath75 7y ago
> even elliptic curves with no rational points on them still have points in finite fields
That’s interesting. How is that possible?
- andrewla 7y agoTake the elliptic curve y^2 = x^3 - 5 that has no rational solutions [1]. But it's easy to see (from brute force) that, for example, 3^2 - 5 = 22 = 27^2 (mod 101). [1] https://kconrad.math.uconn.edu/blurbs/gradnumthy/mordelleqn1.pdf https://kconrad.math.uconn.edu/blurbs/gradnumthy/mordelleqn1...