--- Day changed Wed Sep 14 2016
01:47 < nsh> heh
07:39 < andytoshi> gmaxwell: so i played a bit with j-invariant curves over various small curves. i found a few examples of this duality, a few examples of curves whose orders were the same as their curve orders, and one example with _three_ curves that were related this way
07:40 < andytoshi> (x^3 + 7 = y^2 on F1 had point-group isomorphic to F2; curve eqn on this had group isomorphic to F3; curve eqn on this had group isomorphic to F1)
07:41 < andytoshi> these were not hard to find, i just typed small primes into sage and looked at the group orders, i haven't done any systemic searching, and i moved on whenever i hit a composite order. so i don't have any hypotheses about the general truth..
08:21 < andytoshi> scratch the three-curve thing, i can't find that again, and i think i made a mistake. my experiments show that whenever a j-invariant 0 curve has prime order, there is _some_ "dual curve" on the field of that order, such that the curve order equals the original field order
08:22 < andytoshi> and sometimes there are multiple prime-order fields so you can get chains: like (103, 97) are a pair, as is (97, 79); (79, 67); (67; 73)
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