# QE2 is the list of
# [R, m, sigmas],
# 		where R is the ADE-type of reducible fibers,
# 		m is the sum of the Artin invariant and the torsion rank of Mordell-Weil group, and
# 		sigmas is the set of the possible Artin invariants,
# that are realizable as the triple of 
# an extremal quasi-elliptic K3 surface in characteristic 2.

# QE3 is the list of
# [R, m, sigmas],
# 		where R is the  ADE-type of reducible fibers,
# 		m is the sum of the Artin invariant and the torsion rank of Mordell-Weil group, and
# 		sigmas is the set of the possible Artin invariants,
# that are realizable as the triple of 
# an extremal quasi-elliptic K3 surface in characteristic 3.

# EE is the list of
# [p, R, sigma, MW]
#		where $p$ is the prime integer,
# 		R is the  ADE-type of reducible fibers,
#		sigma is  the Artin invariant, and
#		MW is the Mordell-Weil group,
# that are realizable as the triple of 
# an extremal elliptic K3 surface in characteristic p.




QQE2 := [[D[4]+2*E[8], 1, {1}], [5*A[1]+E[7]+E[8], 3, {2}], [D[12]+E[8], 1, {1

}], [D[4]+D[8]+E[8], 2, {2}], [6*A[1]+D[6]+E[8], 4, {3}], [3*D[4]+E[8], 3, {3}

], [8*A[1]+D[4]+E[8], 5, {4}], [12*A[1]+E[8], 6, {5}], [D[6]+2*E[7], 2, {1}],

[2*A[1]+D[4]+2*E[7], 3, {2}], [6*A[1]+2*E[7], 4, {3}], [3*A[1]+D[10]+E[7], 3,

{1, 2}], [5*A[1]+D[8]+E[7], 4, {2, 3}], [A[1]+2*D[6]+E[7], 3, {2}], [3*A[1]+D[

4]+D[6]+E[7], 4, {2, 3}], [7*A[1]+D[6]+E[7], 5, {3, 4}], [5*A[1]+2*D[4]+E[7],

5, {3, 4}], [9*A[1]+D[4]+E[7], 6, {3, 4, 5}], [13*A[1]+E[7], 7, {4, 5, 6}], [D

[20], 1, {1}], [D[4]+D[16], 2, {1, 2}], [6*A[1]+D[14], 4, {2, 3}], [D[8]+D[12]

, 2, {1, 2}], [2*D[4]+D[12], 3, {2, 3}], [8*A[1]+D[12], 5, {3, 4}], [4*A[1]+D[

6]+D[10], 4, {2, 3}], [6*A[1]+D[4]+D[10], 5, {3, 4}], [10*A[1]+D[10], 6, {4, 5

}], [D[4]+2*D[8], 3, {1, 2, 3}], [6*A[1]+D[6]+D[8], 5, {2, 3, 4}], [3*D[4]+D[8

], 4, {2, 3, 4}], [8*A[1]+D[4]+D[8], 6, {3, 4, 5}], [12*A[1]+D[8], 7, {4, 5, 6

}], [2*A[1]+3*D[6], 4, {1, 2, 3}], [4*A[1]+D[4]+2*D[6], 5, {2, 3, 4}], [8*A[1]

+2*D[6], 6, {3, 4, 5}], [6*A[1]+2*D[4]+D[6], 6, {2, 3, 4, 5}], [10*A[1]+D[4]+D

[6], 7, {3, 4, 5, 6}], [14*A[1]+D[6], 8, {3, 4, 5, 6, 7}], [5*D[4], 5, {1, 2,

3, 4, 5}], [8*A[1]+3*D[4], 7, {2, 3, 4, 5, 6}], [12*A[1]+2*D[4], 8, {3, 4, 5,

6, 7}], [16*A[1]+D[4], 9, {2, 3, 4, 5, 6, 7, 8}], [20*A[1], 10, {3, 4, 5, 6, 7

, 8, 9}]];



QE3 := {[2*E[6]+E[8], 1, 0], [A[2]+3*E[6], 2, 0], [6*A[2]+E[8], 3, 0], [3*A[2]

+E[6]+E[8], 2, 0], [10*A[2], 3, 2], [10*A[2], 5, 0], [A[2]+3*E[6], 1, 1], [6*A

[2]+E[8], 2, 1], [4*A[2]+2*E[6], 3, 0], [7*A[2]+E[6], 4, 0], [10*A[2], 1, 4],

[2*E[8]+2*A[2], 1, 0], [7*A[2]+E[6], 2, 2], [7*A[2]+E[6], 3, 1], [4*A[2]+2*E[6

], 2, 1], [10*A[2], 4, 1], [4*A[2]+2*E[6], 1, 2], [10*A[2], 2, 3]};



EE := {[3, 2*A[5]+D[10], 1, [2, 2]], [7, E[8]+2*A[6], 1, []], [2, 3*A[1]+A[17]

, 1, [6]], [5, A[4]+A[9]+E[7], 1, [2]], [7, A[1]+A[6]+A[13], 1, [2]], [11, 2*A

[10], 1, []], [3, 2*A[2]+D[16], 1, [2]], [2, 4*A[5], 1, [3, 6]], [5, A[2]+A[4]

+A[14], 1, [3]], [3, A[2]+A[11]+D[7], 1, [4]], [2, 2*A[1]+2*A[9], 1, [10]], [2

, A[3]+A[11]+E[6], 1, [6]], [2, A[15]+D[5], 1, [4]]};