?? trying to understand correspondence between extra structure on cuboquadratic alg and on elliptic curve .... ??? ....

??? get cuboquadratic algebra from elliptic curve by ... ?? well, first, seems to make sense to take elliptic curve to have basepoint ... to match small aut gp of cqa ... ?? ... ?? then reverse the branched cover process that gave rise to the ec ... ?? maybe by modding out by inverse involution ??? .... ?? any nice explicit "algebraic" way of doing this ?? .... i was thinking in terms of ... ?? taking subring of functions invariant under inversion ... but perhaps somewhat trickier ... gradedness .... ?? how "theta" line bundle over ec gets along with inversion .... ????? .....

(?? vaguely reminds me of stuff about ... ?? various (??) kinds of "toric" structure on line bundle ... and ... ??? "quantum double" .... ??? .... ??? ...)

?? ... anyway ... thinking perhaps at somewhat naive level ... seems like you can mod out by inverse to get projective line with basepoint ("at infinity" ... ?? ...), aka affine line ..... ??????? ...... ??? translations of which give 1d vsp ??? ..... ???? so that sort of seems to do it .... this 1d vsp is more or less the cuboquadratic alg, we think .... ???? ....

??? might also be able to think of this in some "infinitesimal" way ... ?? take tangent space at some point (..... ???? .....) ..... ??? .....

??? certain sort of pair of cuboquadratic structures, maybe ??? .... ???? .....

?? or ... ?? one elliptic curve being unbranched cover of another .... ???? ..... ?? composite with usual branched cover of sphere by ec .... ??? .....

??? "hecke modular curve" ??? .... ??? "hecke modular function" ???? .... ???? .... relationship to "hecke operator" .... ???? ..... ??? "correspondence" .... ???? .....

???? .......