  We compute the structure of the exotic even nuclei $^{20-34}$Ne and
$^{34-40}$Mg using interactions from chiral effective field theory (EFT). Our
results for the ground-state rotational bands in $^{20-32}$Ne and $^{36-40}$Mg
agree with data. We predict a well-deformed $^{34}$Ne and find that $^{40}$Mg
exhibits an oblate deformed band close to the prolate ground-state, indicating
the emergence of shape co-existence at the neutron dripline. A global
sensitivity analysis shows that the subleading singlet $S$-wave contact and a
pion-nucleon coupling strongly impact deformation in chiral EFT.
