Group 11 element Parkes process. These metals, especially silver, have unusual properties that make them essential for industrial applications outside of their monetary or decorative value. They are all excellent conductors of electricity. The most conductive of all metals are silver, copper and gold in that order. Silver is also the most thermally conductive element, and the most light reflecting element. Silver also has the unusual property that the tarnish that forms on silver is still highly electrically conductive. Copper is used extensively in electrical wiring and circuitry. Gold contacts are sometimes found in precision equipment for their ability to remain corrosion-free. Silver
Conductor of an elliptic curve Conductor of an elliptic curve In mathematics, the conductor of an elliptic curve over the field of rational numbers, or more generally a local or global field, is an integral ideal analogous to the Artin conductor of a Galois representation. It is given as a product of prime ideals, together with associated exponents, which encode the ramification in the field extensions generated by the points of finite order in the group law of the elliptic curve. The primes involved in the conductor are precisely the primes of bad reduction of the curve: this is the Néron–Ogg–Shafarevich criterion. Ogg's formula expresses