address note 24: self-depreciating

Comment:

    Don't say that what you're doing is useless! Just say that a very
    small number of rational points would strengthen the conjecture that
    there is no such rational c.

"Useless" remark is removed, superseded by some closing remarks.

Also add todo comments about double checking the known number of
ratinoal points.
address note 25: N=6 corollary

Comment:

    This result by exhaustion is worth it's own title…. maybe call it
    corollary of the conjecture?

Fully expanded.
add reference for the definition of Jacobian
address note 26: add the 6-cycle to computational...

results

Comment:

    you could mention that in fact this gives a quadratic point, as you
    said at the end of section 4.
address notes 12 and 13: geometric genus

Comment 12:

    you may want to explain that computer algebra softwares can compute
    both geometric and arithmetic genus. Also, the affine model needn't
    be smooth.

Comment 13:

    high GEOMETRIC genus. It could happen that a singular affine model
    has high arithmetic genus but geometric genus 1 or 0.

The genus concept is confusing, since in the definition of the
"geometric" genus, the curve is assumed to be smooth (as least that's
what I found in Qing Liu), but in the REAL WORLD, I have the impression
that everyone is using the "geometric" genus to mean the
GEOMETRIC/ARITHMETIC (which are the same) GENUS OF THE NORMALIZATION,
including the software implementations, while the arithmetic genus
retains its original meaning.

I was trying to simplify the situation by saying that we will only talk
about the geometric genus of the normalization from now on, but that
seems to be a failed attempt for people who are already familiar with
the concepts (they will typically ignore the author's idiosyncrasies).

Therefore, in this change set, I tried to make every reference to a
curve (smooth or not?) and a genus (arithmetic or geometric?
normalization?) as explicit as possible.