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Sunday, June 15, 2025

Entry 172

There are many fundamental d=4m with class number 8, though only seven are prime namely p=41,113,137,313,337,457,577. Their Ramanujan G-functions are

G41=(x+x242)1/2=x24+x+24G113=(y+y242)1/2=y24+y+24 where x=(5+414)(1+5+418)y=(9+1134)(1+7+1132) and similarly for the other p, though the quartic roots get more complicated.

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