There are four elliptic curves, which were generated at the same time, and which have similar properties: secp160k1, secp192k1, secp224k1, and secp256k1. If you calculate half of the generator, then you can see this:
secp160k1: 48ce563f89a0ed9414f5aa28ad0d96d6795f9c62
secp192k1: 0554123b78ce563f89a0ed9414f5aa28ad0d96d6795f9c66
secp224k1: 3b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63
secp256k1: 3b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63
Currently, even secp160k1 was still not yet broken, so we probably should start from that. Maybe even there could be more curves, designed specifically as a challenge, for example something like that: curves1000/bits at master · vjudeu/curves1000 · GitHub
Which means, that we could have 128-bit curve, then 129-bit curve, and so on, up to some 255-bit curve.