How grouping by conductor reveals murmuration patterns
The conductor N summarizes "bad" primes for a curve. Grouping by N normalizes curves so their aₚ values become comparable, revealing statistical patterns.
Pozdnyakov's crucial insight was to NOT normalize aₚ values by √p, which experts traditionally did. This preserved the oscillations that became visible as murmurations.
The original discovery used data from the LMFDB (L-functions and Modular Forms Database), which conveniently pre-sorts curves by conductor.