Recently, I was quite surprised, when I saw that there are six different n-values, matching different b-values in secp256k1:
+-----+---------------------------------------------------------------------+
| b | n |
+-----+---------------------------------------------------------------------+
| 0x7 | 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141 |
+-----+---------------------------------------------------------------------+
The question is: does it mean that there is some kind of connection between y^2=x^3+7, and for example y^2=x^3+2? Or maybe there is another connection, where points on curves with identical p-value and n-value can be mapped? Does it mean, that if we have b=0x7, where there are "n" points, and for example b=0xc curve also has the same amount of points, then does it mean we can map them 1:1?
Not very sure about the 1:1 mapping although, previously i saw when b = 0x0, it leads to a very simplified loop which allowed to map from Pubkey to Privatekey. However I could not find any way to map b = 0x7 curve pubkey into a b = 0x0 curve pubkey.