line of 1/5(1,4)
  a,2a,3a,b,3a,2a,a

Conj 1.  deg Ga = 3a - b
Conj 2.  deg E1-E4 = 4a + 2b

[1,1,4,5,5,16],
d := 16; A:=[1,1,4,5,5]; B:=[];
D := P(d,A) - PA(A) - Pb(B);
 Denominator(D) eq &*[1-t^i : i in [1,1,5,5]]; // true
 Numerator(D); // 2*t^9+4*t^8+6*t^7+5*t^6+6*t^5+4*t^4+2*t^3
 // 2,4,6,5, deg Ga = 1/5^2
 // E1 = Oh(-1,-1+16) = Oh(14), E4 = Oh(-4), E1-E4 = Oh(18), deg = 18*/5^2

[1,1,4,5,10,21],
d := 21; A:=[1,1,4,5,10]; B:=[];
D := P(d,A) - PA(A) - Pb(B) - Phalfc()/4*10 - Pemb2(2);
 // This one has emb 1/10(1,4,5)

[1,1,4,10,15,31], // emb 1/10 and 1/15
[1,4,4,5,10,24], // emb 1/10
[1,4,5,5,5,20],
d := 20; A:=[1,4,5,5,5]; B:=[];
D := P(d,A) - PA(A) - Pb(B);
 // 2*t^9+4*t^8+6*t^7+2*t^6+6*t^5+4*t^4+2*t^3
 // 2,4,6,2, deg Ga = 4/5^2
 // E1 = Oh(-1), E4 = Oh(-4), E1-E4 = Oh(3), deg = 12/5^2

[1,4,5,5,10,25], emb 1/10(1,4,5_
[1,4,5,5,14,29],
d:=29; A:=[1,4,5,5,14]; B:=[];
D := P(d,A) - PA(A) - Pb(B) -Phalfc()/4*14 - Pemb2(2) - Pemb2(7);
  // the emb pt at 14 is 1/14(4,5,5)

[1,4,5,10,10,30], has emb 3 x 1/10
[1,4,5,10,16,36],
[1,4,5,10,20,40],
[1,4,5,15,20,45],
[1,4,5,15,24,49],
[1,4,5,20,30,60],
[1,4,10,10,15,40],
[1,4,10,10,25,50],
[1,4,10,15,15,45],
[1,4,10,15,30,60],
[1,4,10,20,25,60],
[1,4,10,25,36,76],
[1,4,10,30,45,90],
[1,4,15,20,20,60],
[1,4,15,20,25,65],
[1,4,15,20,36,76],
[1,4,15,20,39,79],
[1,4,15,20,40,80],
[1,4,15,40,60,120],
[1,4,20,25,30,80],
[1,4,20,25,50,100],
[1,4,30,40,45,120],
[1,5,6,9,15,36],
[1,5,9,10,16,41],
[1,5,9,10,25,50],
d:=50; A:=[1,5,9,10,25]; B:=[[9,1,1,7]];
D := P(d,A) - PA(A) - Pb(B);
 // t^9+2*t^8+3*t^7+2*t^6+3*t^5+2*t^4+t^3
 // 1,2,3,2, deg Ga = 1/5^2
 // E1 = Oh(-1), E4 = Oh(-9), E1-E4 = Oh(8), deg 8/5^2

[1,5,9,15,15,45],
[1,5,9,15,21,51],
[1,5,9,15,25,55],
[1,5,9,15,29,59],
[1,5,9,15,30,60],
[1,5,9,30,45,90],
[1,5,14,25,44,89],
[1,5,14,35,50,105],
[1,5,19,25,45,95],
[1,5,19,25,50,100],
[1,5,19,45,70,140],
[1,5,24,30,36,96],
[1,5,24,30,60,120],
[1,5,24,60,90,180],
[1,5,29,40,46,121],
[1,5,34,45,51,136],
[1,6,9,25,40,81],
[1,9,10,15,25,60],
[1,9,10,30,40,90],
[1,9,10,30,41,91],
[1,9,10,30,49,99],
[1,9,10,30,50,100],
[1,9,15,15,20,60],
[1,9,15,20,36,81],
[1,9,15,25,49,99],
[1,9,15,25,50,100],
[1,9,15,50,75,150],
[1,10,10,14,35,70],
[1,10,14,35,59,119],
[1,10,14,50,75,150],
[1,10,24,30,55,120],
[1,10,24,60,85,180],
[1,10,34,40,85,170],
[1,10,34,45,80,170],
[1,10,34,45,90,180],
[1,10,34,80,125,250],
[1,10,44,55,110,220],
[1,10,44,110,165,330],
[1,10,54,75,86,226],
[1,11,24,60,85,181],
[1,14,20,35,70,140],
[1,14,20,70,105,210],
[1,14,30,75,106,226],
[1,14,45,75,90,225],
[1,15,19,25,41,101],
[1,15,19,70,105,210],
[1,15,20,24,60,120],
[1,15,24,40,40,120],
[1,15,24,40,56,136],
[1,15,24,40,65,145],
[1,15,24,40,79,159],
[1,15,24,80,120,240],
[1,15,34,85,120,255],
[1,15,49,65,81,211],
[1,15,49,65,115,245],
[1,15,49,65,130,260],
[1,15,49,115,180,360],
[1,15,64,80,160,320],
[1,15,64,160,240,480],
[1,16,25,29,70,141],
[1,16,34,40,45,136],
[1,16,34,85,120,256],
[1,20,44,55,100,220],
[1,20,64,75,160,320],
[1,20,64,85,150,320],
[1,20,64,85,170,340],
[1,20,84,105,210,420],
[1,24,75,200,300,600],
[1,24,150,200,225,600],
[1,30,64,80,145,320],
[1,30,64,160,225,480],
[1,30,78,140,171,420],
[1,30,94,110,235,470],
[1,30,94,220,345,690],
[1,30,124,310,465,930],



line of 1/5(2,3)
[2,2,3,5,10,22], emb 1/10
[2,2,5,8,15,32], emb 1/15
[2,2,10,13,25,52], emb 1/10 and 1/25
[2,3,3,5,5,18],
d := 18; A:=[2,3,3,5,5]; B:=[[3,2,2,2] : i in [1..6]];
D := P(d,A) - PA(A) - Pb(B);
Denominator(D) eq &*[1-t^i : i in [1,1,5,5]]; // true
 // 4*t^9+t^8+6*t^7+4*t^6+6*t^5+t^4+4*t^3
 // 4,1,6,4, deg Ga = 1
 // E2 = Oh(-2); E3 = Oh(-3,-3+18) = Oh(12); E2-E3 = Oh(-14)

[2,3,3,10,15,33],
[2,3,5,5,5,20],
d:=20; A:=[2,3,5,5,5]; B:=[[3,2,2,2]];
D := P(d,A) - PA(A) - Pb(B);
Denominator(D) eq &*[1-t^i : i in [1,1,5,5]]; // true
Numerator(D); // -2*t^9-2*t^8-8*t^6-2*t^4-2*t^3
// -2,-2,0,-8
// deg Ga = 4/5^2
// E2 = Oh(-2), E3 := Oh(-3); E2-E3 = Oh(1);

[2,3,5,5,15,30],
d:=30; A:=[2,3,5,5,15]; B:=[[3,2,2,2],[3,2,2,2]];
D := P(d,A) - PA(A) - Pb(B); // -t^9-t^8-4*t^6-t^4-t^3
// -1,-1,0,-4
// deg Ga = 2/5^2
// E2 = Oh(-2), E3 := Oh(-3); E2-E3 = Oh(1);

[2,3,5,5,10,25],
[2,3,5,5,12,27],
d:=27; A:=[2,3,5,5,12]; B:=[[3,2,2,2],[3,2,2,2]]; // also curve of 2 with emb 1/12
D := P(d,A) - PA(A) - Pb(B) - 1/(2*12)*Phalfc() - c12255; not finished

[2,3,5,5,13,28]
d:=28; A:=[2,3,5,5,13]; B:=[[3,2,2,2],[13,3,5,5]]; 
D := P(d,A) - PA(A) - Pb(B);
 // 4*t^9 + t^8 + 6*t^7 + 4*t^6 + 6*t^5 + t^4 + 4*t^3
 // 4,1,6,4, deg Ga = 1
 // E2 = Oh(-2), E3 := (-3,-13,+28) = Oh(12)
 
[2,3,5,10,10,30],
[2,3,5,10,18,38],
[2,3,5,10,20,40],
[2,3,5,15,20,45],
[2,3,5,15,22,47],
[2,3,5,15,23,48],
[2,3,5,15,25,50],
[2,3,5,20,30,60],
[2,3,7,15,25,52],
[2,3,8,15,20,48],
[2,3,10,10,15,40],
[2,3,10,10,25,50],
[2,3,10,15,15,45],
[2,3,10,15,20,50],
[2,3,10,15,30,60],
[2,3,10,20,25,60],
[2,3,10,25,38,78],
[2,3,10,30,45,90],
[2,3,12,20,35,72],
[2,3,15,20,20,60],
[2,3,15,20,38,78],
[2,3,15,20,40,80],
[2,3,15,25,30,75],
[2,3,15,25,45,90],
[2,3,15,40,60,120],
[2,3,20,25,30,80],
[2,3,20,25,50,100],
[2,3,20,30,35,90],
[2,3,20,30,55,110],
[2,3,20,50,75,150],
[2,3,30,40,45,120],
[2,3,30,40,75,150],
[2,5,5,8,20,40],
d:=40; A:=[2,5,5,8,20]; B:= []; // curve of 1/2 of deg 1/8 with emb 1/4
D := P(d,A) - PA(A) - Pb(B) - 1/8*Phalfc() - Pemb2(2);
 // -4*t^9-2*t^8-4*t^7-8*t^6-4*t^5-2*t^4-4*t^3
 // -4,-2,-4,-8
 // deg Ga = 2/5^2
 // E2 = Oh(-2), E3 = Oh(-8), E2-E3 = Oh(6)

[2,5,5,8,12,32],
d:=32; A:=[2,5,5,8,12]; B:=[];
D := P(d,A) - PA(A) - Pb(B) - 32/(2*8*12)*Phalfc() - c12255;
 
[2,5,8,10,15,40],
[2,5,8,10,17,42],
[2,5,8,10,23,48],
[2,5,8,10,25,50],
d := 50; A:=[2,5,8,10,25]; B:=[]; // curve of 1/2 of deg 5/16 with emb 1/8(1,2,5)
// digress
// c8125 := (-3/4*t^9+1/4*t^7-t^6+1/4*t^5-3/4*t^3)/&*[1-t^i : i in [1,1,1,8]];
// that is slightly wrong
D := P(d,A) - PA(A) - Pb(B) - 5/16*Phalfc() - c8125;
// -2*t^9-t^8-2*t^7-4*t^6-2*t^5-t^4-2*t^3
// -2,-1,-2,-4
// deg Ga = 1/5^2
// E2 = Oh(-2), E3 := Oh(-8), E2-E3 = Oh(6)

// digress some more to get c8125
[1,1,2,5,8,17],
d := 17; A:=[1,1,2,5,8]; B:=[[5,1,1,3]];
D:= P(d,A)-PA(A)-Pb(B)-1/16*Phalfc();
c8125 := D;

[2,5,8,15,15,45],
d:=45; A:=[2,5,8,15,15]; B:=[]; // curve of 1/2 of deg 1/16 with emb 1/8(2,7,7)
// curve of 1/5(2,3) with emb 3 x 1/15
D := P(d,A) - PA(A) - Pb(B) - 5/16*Phalfc() - c8277;

// digress to get c8277
[2,4,7,7,8,28],
d := 28; A:=[2,4,7,7,8]; B:=[[7,1,2,4] : i in [1..4]];
// curve of 2 with emb 1/8(2,7,7) and 3 x 1/4(2,3,3)
D := P(d,A) - PA(A) - Pb(B) - 28/(2*4*8)*Phalfc() - 3*c4233;

// digress further to get c4233;
[2,3,3,3,4,15],
d := 15; A:=[2,3,3,3,4]; B:=[];
D := P(d,A) - PA(A) - Pb(B) + 5*t^4/&*[1-t^i : i in [1,1,3,3]];
gives
c4233 := (-t^5-t^4-t^3)/ &*[1-t^i : i in [1,1,2,4]];

[2,7,8,12,27,56],
d:=56; A := [2,7,8,12,27];

[2,7,8,16,31,64],
d:=64; A:=[2,7,8,16,31]; B:= [[7,2,2,3],[31,7,8,16]];
D := P(d,A) - PA(A) - Pb(B) - 56/(2*7*8)*Phalfc() - 4*c8277;
// Denom is &*[1-t^i : i in [1,1,2,8]];
// -2*t^9 - 4*t^8 - 2*t^7 - 4*t^6 - 2*t^5 - 4*t^4 - 2*t^3
// -t^8 - t^6 - t^4
c8277 := 1/8*Phalfc() + (-t^4-t^6-t^8)/&*[1-t^i : i in [1,1,2,8]];

[2,5,8,15,25,55],
[2,5,8,20,33,68],
[2,5,8,25,35,75],
[2,5,8,25,40,80],
[2,5,8,30,45,90],
[2,30,126,157,315,630],
d := 630; A:=[2,30,126,157,315];B:=[[157,1,30,126]];
// hopeless


lines of 10
[1,9,20,30,40,100],
[1,9,20,30,60,120],
[1,9,20,60,90,180],
[1,19,30,70,90,210],