Diophantine Equation

BBdio(H) is the maximum score among all solvable polynomial Diophantine equations of height H. To determine the height of an equation, write it in the form P(x,y,z,...) = 0, then take the sum of |coefficient|*2^degree among all terms in the LHS polynomial P. To determine the score of a solvable equation, find the solution with the lowest score, where the score of a solution is the maximum absolute value among all variables.

BBdio(n) is proven for n < 16.

BBdio(n)	Value	Champion
2 ≤ n ≤ 20	≥ n-2
21	≥ 26	$x^2+xy+6y+1=0$
22	≥ 22	$x^3+y^2+4=3x$
23	≥ 31	$x^2+xy+x+1=6y$
24	≥ 66	$x^3+xy+5y=2$
25	≥ 470	$x^3+xy+y^2+y+7=0$
26	≥ 40	$x^2+xy+7y+4=0$
27	≥ 849	$x^3+x^2+y^2+9=x$
28	≥ 74	$x^3+xy+2x+5y=2$
29	≥ 221	$x^3+xy+x+7y+1=0$
30	≥ 849	$x^3+2x^2=y^2+10$