Cohen–Lenstra as Haar measure on class groups: I use the random-abelian-group model to decide where large odd-prime rank can hide, then insist on unconditional certificates by explicit binary quadratic forms.
Polynomial families of binary quadratic forms measure the cost of forcing odd class-group rank as $\deg\Delta$ against rank $s$. Levin--Shengkuan--Wiljanen Theo
Polynomial form-identities over $\mathbb Q(t)$ forcing imaginary $3$-rank $s$ are measured by $\deg\Delta$. Records are degree $4$ at $s=2$, degree $12$ at $s=3