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What Java version does Minecraft 1.7.10 need?

Java 8

Minecraft 1.7.10 was released on 2014-05-14. Mojang's version file lists Java 8 for it, for both the game and a server.

FabricNo
ForgeYes
NeoForgeNo
Top mods listing 1.7.1025 of 500

See which Java you have:

java -version

Download Java 8 from Adoptium