None only when it becomes Gyrados can it learn TM's.
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No, you must evolve Magikarp into Gyarados for it to learn Hyper Beam. (Magikarp can't learn any TMs)
Magikarp can't learn any TM moves.
Gyarados should learn Bite once Magikarp evolves at lv 20. Gyarados will then learn Dragon Rage at 25, Leer at 32, Hydro Pump at 41, and Hyper Beam at 52. Gyarados will also learn moves if you teach it TMs and HMs.
MagikarpActually, Magikarp can learn moves and level up. Magikarp can learn Tackle and Flail. Feebas can also learn Tackle and Splash. Magikarp and Feebas can't learn any more moves until they evolve into Gyarados or Milotic.
no