In SEC 2: Recommended Elliptic Curve Domain Parameters curve secp112r1 has $0xDB7C2ABF62E35E668076BEAD208B$ as the order of the finite field and as the $a$ coefficient in the equation $y^2 =x^3 +ax +b$. Wouldn't that essentially make the $a$ coefficient $0$? If so then why not just say that that's what the coefficient is?

secp192k1 has $0$ as coefficients so it's not like there's not precedent for a coefficient of $0$.


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You misread the parameters: $p$ is $$\mathrm{0xDB7C2ABF62E35E668076BEAD208B} \text,$$ but $a$ is $$\mathrm{0xDB7C2ABF62E35E668076BEAD208\underline{\mathbf8}}$$ which is $-3$ $\bmod p$!


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