It is conjectured that, if one of these objects has an infinite number of solutions, then an associated L-function constructed from the Euler product of the points lying on it modulo a prime p will equal zero when the complex variable equals one. The rational points of these objects have a finite basis by Mordell's theorem. Over the complex numbers, these objects correspond to embedding tori in the complex projective plane. A theorem relating these objects over the field of rationals to modular forms was instrumental in Wiles' proof of Fermat's last theorem. For 10 points, name these curves given by an equation of the form y squared equals x cubed plus A x plus B.
It is conjectured that, if one of these objects has an infinite number of solutions, then an associated L-function constructed from the Euler product of the points lying on it modulo a prime p will equal zero when the complex variable equals one. The rational points of these objects have a finite basis by Mordell's theorem. Over the complex numbers, these objects correspond to embedding tori in the complex projective plane. A theorem relating these objects over the field of rationals to modular forms was instrumental in Wiles' proof of Fermat's last theorem. For 10 points, name these curves given by an equation of the form y squared equals x cubed plus A x plus B.
It is conjectured that, if one of these objects has an infinite number of solutions, then an associated L-function constructed from the Euler product of the points lying on it modulo a prime p will equal zero when the complex variable equals one.