What's the code for doing the reverse of this code over the altbn128 curve

The altbn254 curve is defined here : 
https://github.com/ethereum/EIPs/blob/master/EIPS/eip-197.md#definition-of-the-groups

This is the code responsible for mapping points from F_p² to F_p¹² :

  p=21888242871839275222246405745257275088696311157297823662689037894645226208583;
  i=ffgen((i^2+1)*Mod(1,p));
  X=11559732032986387107991004021392285783925812861821192530917403151452391805634*i+10857046999023057135944570762232829481370756359578518086990519993285655852781;
  Y=4082367875863433681332203403145435568316851327593401208105741076214120093531*i+8495653923123431417604973247489272438418190587263600148770280649306958101930;
  pt = [X,Y];
  \\ then define the target field, the target curve and the map from Fp[i] to Fp[w]:
  w=ffgen((w^12 - 18 * w^6 + 82)*Mod(1,p));
  E2 = ellinit([0,3],w);
  map = ffembed(i,w);
  \\ define the isomorphism:
  twist(pt)= [ffmap(map,pt[1])*w^2, ffmap(map,pt[2])*w^3];
  \\ apply to pt
  pt2=twist(pt);
  \\ check
  ellisoncurve(E2,pt2)
  %11 = 1
  \\ success!


But now given a valid pt2 over the curve E2, how to ffmap it back to pt 
over the curve defined over the i finite field ?

Of course, I understand this can only happen if pt has the suitable 
order of 
|21888242871839275222246405745257275088548364400416034343698204186575808495617|.