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We present an improved algorithm for tabulating class groups of imaginaryquadratic fields of bounded discriminant. Our method uses classical classnumber formulas involving theta-series to compute the group ordersunconditionally for all $\Delta \not \equiv 1 \pmod{8}.$ The group structure isresolved using the factorization of the group order. The $1 \bmod 8$ case washandled using the methods of \cite{jacobson}, including the batch verificationmethod based on the Eichler-Selberg trace formula to remove dependence on theExtended Riemann Hypothesis. Our new method enabled us to extend the previousbound of $|\Delta| < 2 \cdot 10^{11}$ to $2^{40}$. Statistical data in supportof a variety conjectures is presented, along with new examples of class groupswith exotic structures.

Unconditional Class Group Tabulation of Imaginary Quadratic Fields to $|\Delta| < 2^{40}$