  We construct the free Lagrangian of the magnetic sector of Carrollian
electrodynamics. The construction relies on Helmholtz integrability condition
for differential equations in a self consistent algorithm, working hand in hand
with imposing invariance under infinite dimensional Conformal Carroll algebra.
It requires inclusion of new fields in the dynamics and the system is free of
gauge redundancies. We next add interaction (quartic) terms to the free
Lagrangian, strictly constrained by conformal invariance and Carrollian
symmetry. The dynamical realization of the non-semi simple infinite dimensional
symmetry algebra at the level of charge algebra is exact and free from central
terms.
