Generation VOther generations:NoneLevelMoveTypeCat.Pwr.Acc.PPStartU-turnBugPhysical70100%20StartScratchNormalPhysical40100%35StartLeerNormalStatus-100%30StartPursuitDarkPhysical40100%20StartHone ClawsDarkStatus--%155PursuitDarkPhysical40100%209Hone ClawsDarkStatus--%1513Fury SwipesNormalPhysical1880%1517Faint AttackDarkPhysical60-%2021Scary FaceNormalStatus-100%1025TauntDarkStatus-100%2029Foul PlayDarkPhysical95100%1530Night SlashDarkPhysical70100%1534TormentDarkStatus-100%1539AgilityPsychicStatus--%3044EmbargoDarkStatus-100%1549PunishmentDarkPhysical-100%554Nasty PlotDarkStatus--%2059ImprisonPsychicStatus--%1064Night BurstDarkSpecial8595
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it can learn Grass and Psychic moves
ZOROARK
No.Magikarp cannot learn any TM moves if it evolves into gyarados then gyarados can learn TM moves and HM moves too. I Hope i helped you!
No Pokemon can learn more than four moves.
Magikarp can't learn any TM moves.