  We construct a smooth Artin stack parameterizing the stable weighted curves
of genus one with twisted fields and prove that it is isomorphic to the blowup
stack of the moduli of genus one weighted curves studied by Hu and Li. This
leads to a blowup-free construction of Vakil-Zinger's desingularization of the
moduli of genus one stable maps to projective spaces. This construction
provides the cornerstone of the theory of stacks with twisted fields, which is
thoroughly studied in arXiv:2005.03384 and leads to a blowup-free resolution of
the stable map moduli of genus two.
