The pickups generate the hum, not the amp.
Any amp will make the pickup hum.
Mostly true, but some amps have circuit quirks that turn them into an AM antenna, particularly once a guitar is hooked up. Especially with flawed tubes, other out of spec components, bad grounding.
And even humbuckers don't help with certain types of noise, like from dimmer switches and nearby radio transmitters (including noisy AC motors, etc).
Many amps will translate power line noise into signal, too, which can be all kinds of fun to sort out.
There's lots of reasons a lot of touring bands use power conditioners, and ground fault isolators are in many studio/engineer toolkits. Along with quality shielded cables. A bad cable can act as an antenna all by itself.
Checking your power is correctly wired is important to protect your gear as well as safety. A basic wiring correctness tester is pretty cheap now.
Without more information, determining what the problem is can only be speculation, though. Are external effects involved, or straight to amp? What is house wiring like? Are there dimmers, neon signs, HVAC, microwave, old wireless phones & walkie talkies, nearby AM Radio stations, etc all in operation at once nearby?