Please explain parameters of RFC5639 Elliptic Curves including brainpoolP160r1
The order of the curve $\#E(\mathbb{F}_p)$ is different from $p$. In fact, according to Hasse's theorem, $\#E(\mathbb{F}_p)=p+1-t$ where $t$ the Frobenius trace satisfies $|t|&lt;2\sqrt{p}$. So the gap between $\#E(\mathbb{F}_p)$ and $p$ is at most $2\sqrt{p}$. Note that, if $\#E(\mathbb{F}_p)=p+1$, $\textit{i.e.}$ $t=0$, the curve is supersingular. For brainpoolP160r1, the order is 1332297598440044874827085038830181364212942568457 (160-bit). You can play with sage code:

p = 0xE95E4A5F737059DC60DFC7AD95B3D8139515620F 
A = 0x340E7BE2A280EB74E2BE61BADA745D97E8F7C300
B = 0x1E589A8595423412134FAA2DBDEC95C8D8675E58
x = 0xBED5AF16EA3F6A4F62938C4631EB5AF7BDBCDBC3
y = 0x1667CB477A1A8EC338F94741669C976316DA6321
E = EllipticCurve(GF(p),[A,B])
G = E(x,y)
G.order()
E.order()