Can I run gemma-4-E2B-it-GGUF on an RTX 5070?

Yes, just

Its BF16 file (9.31 GB) fits in the 10.8 GB an RTX 5070 can use, with room for ≈ 99K tokens of context.

ollama run hf.co/unsloth/gemma-4-E2B-it-GGUF:BF16

Files and context on RTX 5070

Each file of gemma-4-E2B-it-GGUF (and of GGUF versions the site has analyzed), and how much context fits next to it, with the context cache in 16-bit or 8-bit.

gemma-4-E2B-it-GGUF on other hardware

Popular models that run on RTX 5070

Assumes 90% of the card's memory is usable and at least 4K tokens of context for one conversation, with the context cache in 16-bit unless noted. Fits leaves at least 20% of that memory for context; Tight leaves less.