This continues Entry 112. Recall the modular lambda function λ(τ) λ(τ)=(√2η(12τ)η2(2τ)η3(τ))8 We chose fundamental discriminants d=4m with class number h(−d)=4 for even m with eight divisors, hence only m=30,42,78,102, and m=70,130,190 which are evenly divisible by 3 and 5, respectively. 1√λ(√−30)=(2+√3)(5+2√6)(4+√15)√11+2√301√λ(√−42)=(2+√3)2(1+√2)2(8+3√7)√13+2√421√λ(√−78)=(2+√3)3(5+2√6)(25+4√39)√53+6√781√λ(√−102)=(2+√3)2(5+2√6)2(50+7√51)√101+10√102 as well as 1√λ(√−70)=(8+3√7)(15+4√14)(6+√35)√251+30√701√λ(√−130)=(1+√2)4(3+√10)2(5+√26)(57+5√130)1√λ(√−190)=(170+39√19)(37+6√38)(39+4√95)√52021+3774√190
For the last, note that U190=52021+3774√190=(51√10+37√19)2 and similarly for other Un with composite n but I chose to retain the a+b√n form. Most of these do not appear in Mathworld's list. Arranged by class number, one can see some patterns like the m have eight divisors and λ(τ) is a product of four Un. Next are m that have sixteen divisors and λ(τ) is a product of eight Un.
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