Index  Tamagawa number  bad reduction  Cauchy  cochain  complete  congruent  elliptic curve  formal group  morphism  good reduction  Hilbert 90  integral  isogeny  isogenous  j invariant  linearly equivalent  minimal  Mordell Weil  bad reduction  good reduction  primitive  quadratic form  rational  rational  separable  elliptic curve  unramified  Weierstrass equation  Weierstrass form  Weak Mordell Weil Theorem