What Is An Elliptic Curve?

• An elliptic curve is a cubic curve where a and b are integers and

• The conductor of E is an integer divisible only by primes that divide disc(E):

  • The powers of the primes that divide the conductor encode information about what the graph of E looks like modulo those primes.
  • There are only finitely many "essentially different" elliptic curves with a given conductor.

Notes: