K:=NumberField(x^2-x+1); R:=MaximalOrder(K); function tzi(ai,n) E:=EllipticCurve(ai);//ai; if BaseRing(E) eq Q then E:=BaseChange(E,K); end if; return >; end function; tzi([0 ,1 + w , w , w ,0 ] , 3 + 5*w ); tzi([1 ,1 + w ,0 , w ,0 ] , 8 + w ); tzi([1 ,1 + w ,0 ,-4*w ,4 -9*w ] , 8 + w ); tzi([1 ,1 + w ,0 ,10 +6*w ,20 -11*w ] , 8 + w ); tzi([1 ,1 + w ,0 ,5 +11*w ,11 -20*w ] , 8 + w ); tzi([1 + w , w ,0 ,-1 + w ,0 ] , 5 + 5*w ); tzi([1 + w , w ,0 ,4 -4*w ,7 ] , 5 + 5*w ); tzi([1 + w , w ,0 ,79 -79*w ,322 ] , 5 + 5*w ); tzi([1 + w , w ,0 ,9 -9*w ,0 ] , 5 + 5*w ); tzi([1 + w , w ,0 ,134 -134*w ,-525 ] , 5 + 5*w ); tzi([1 + w , w ,0 ,-36 +36*w ,-63 ] , 5 + 5*w ); tzi([1 + w , w ,0 ,2159 -2159*w ,-37380 ] , 5 + 5*w ); tzi([1 + w , w ,0 ,109 -109*w ,-770 ] , 5 + 5*w ); tzi([0 ,0 ,1 ,0 ,0 ] , 9 ); tzi([0 ,0 ,1 ,-30 ,63 ] , 9 ); tzi([0 ,-1 ,1 ,0 ,0 ] , 11 ); tzi([0 ,-1 ,1 ,-10 ,-20 ] , 11 ); tzi([0 ,-1 ,1 ,-7820 ,-263580 ] , 11 ); tzi([ w ,-1 + w ,1 + w , -w , -w ] , 10 + 2*w ); tzi([ w ,-1 + w ,1 + w ,10 +4*w ,6 +2*w ] , 10 + 2*w ); tzi([ w ,-1 + w ,1 + w ,-750 -551*w ,-5980 -10551*w ] , 10 + 2*w ); tzi([0 ,0 ,0 ,0 ,1 ] , 12 ); tzi([0 ,0 ,0 ,-15 ,22 ] , 12 ); tzi([1 + w , -w ,0 ,-1 + w ,0 ] , 7 + 7*w ); tzi([1 + w , -w ,0 ,4 -4*w ,-1 ] , 7 + 7*w ); tzi([1 + w , -w ,0 ,49 -49*w ,-136 ] , 7 + 7*w ); tzi([1 + w , -w ,0 ,39 -39*w ,90 ] , 7 + 7*w ); tzi([1 + w , -w ,0 ,784 -784*w ,-8515 ] , 7 + 7*w ); tzi([1 + w , -w ,0 ,34 -34*w ,-217 ] , 7 + 7*w ); tzi([1 + w , -w ,0 ,-321 -149*w ,-1906 -1866*w ] , 7 + 7*w ); tzi([1 + w , -w ,0 ,149 +321*w ,-3772 +1866*w ] , 7 + 7*w ); tzi([1 + w ,0 , w ,0 ,0 ] , 9 + 6*w ); tzi([1 + w ,0 , w ,-5 +10*w ,1 +10*w ] , 9 + 6*w ); tzi([1 + w ,0 , w ,5 -10*w ,13 -10*w ] , 9 + 6*w ); tzi([1 + w ,0 , w ,-25 +5*w ,67 -19*w ] , 9 + 6*w ); tzi([0 , w ,0 ,-1 + w ,0 ] , 8 + 8*w ); tzi([0 , w ,0 ,-11 +6*w ,10 -11*w ] , 8 + 8*w ); tzi([0 , w ,0 ,-6 +11*w ,-1 +11*w ] , 8 + 8*w ); tzi([0 , w ,0 ,4 -4*w ,4 ] , 8 + 8*w ); tzi([0 , w ,0 ,64 -64*w ,220 ] , 8 + 8*w ); tzi([0 , w ,0 ,24 -24*w ,-36 ] , 8 + 8*w ); tzi([0 , w ,0 ,384 -384*w ,-2772 ] , 8 + 8*w ); tzi([0 , w ,0 ,-16 +16*w ,-180 ] , 8 + 8*w ); tzi([ w ,0 ,1 ,0 ,0 ] , 14 ); tzi([ w ,0 ,1 ,10*w ,12 ] , 14 ); tzi([ w ,0 ,1 ,-5*w ,-6 ] , 14 ); tzi([ w ,0 ,1 ,35*w ,-70 ] , 14 ); tzi([ w ,0 ,1 ,220 -405*w ,-2854 +1920*w ] , 14 ); tzi([ w ,0 ,1 ,-220 -185*w ,-934 -1920*w ] , 14 ); tzi([ w ,0 ,1 ,170*w ,-874 ] , 14 ); tzi([ w ,0 ,1 ,2730*w ,-55146 ] , 14 ); tzi([ w ,0 ,1 ,-230 -185*w ,-806 -1880*w ] , 14 ); tzi([ w ,0 ,1 ,230 -415*w ,-2686 +1880*w ] , 14 ); tzi([1 + w ,1 ,1 ,-1 , -w ] , 14 + 2*w ); tzi([1 + w ,1 ,1 ,9 ,8 -9*w ] , 14 + 2*w ); tzi([1 + w ,1 ,1 ,-36 +55*w ,-54 +167*w ] , 14 + 2*w ); tzi([1 + w ,1 ,1 ,-36 -105*w ,266 +615*w ] , 14 + 2*w ); tzi([1 + w ,1 + w ,1 + w ,-1 + w ,-1 ] , 15 + w ); tzi([1 + w ,1 + w ,1 + w ,-1 +6*w ,-8 +4*w ] , 15 + w ); tzi([1 + w ,1 + w ,1 + w ,-6 +86*w ,-327 +47*w ] , 15 + w ); tzi([1 + w ,1 + w ,1 + w ,4 +6*w ,3 -3*w ] , 15 + w ); tzi([0 ,-1 - w ,0 , w ,0 ] , 16 ); tzi([0 ,-1 - w ,0 ,-4*w ,-4 +8*w ] , 16 ); tzi([1 + w ,1 - w ,1 + w ,-2*w , -w ] , 16 + w ); tzi([1 + w ,1 - w ,1 + w ,-5 -2*w ,3 ] , 16 + w ); tzi([1 + w ,1 - w ,1 + w ,-85 -7*w ,274 +34*w ] , 16 + w ); tzi([1 + w ,1 - w ,1 + w ,-5 +3*w ,4 +10*w ] , 16 + w ); tzi([1 + w ,1 - w ,1 + w ,-80 +123*w ,-11 +475*w ] , 16 + w ); tzi([1 + w ,1 - w ,1 + w ,70 -37*w ,63 +125*w ] , 16 + w ); tzi([1 + w ,1 - w ,1 + w ,1090 -542*w ,3564 +8949*w ] , 16 + w ); tzi([1 + w ,1 - w ,1 + w ,250 -172*w ,-702 -559*w ] , 16 + w ); tzi([1 ,1 + w ,1 ,-1 + w ,-1 ] , 11 + 8*w ); tzi([1 ,1 + w ,1 ,-1 +6*w ,-5 +2*w ] , 11 + 8*w ); tzi([1 ,1 + w ,1 ,9 -34*w ,-47 +50*w ] , 11 + 8*w ); tzi([1 ,1 + w ,1 ,-16 +81*w ,-227 -22*w ] , 11 + 8*w ); tzi([1 ,1 + w ,1 ,14 +11*w ,41 -26*w ] , 11 + 8*w ); tzi([1 ,1 + w ,1 ,14 -39*w ,-17 +38*w ] , 11 + 8*w ); tzi([1 ,1 + w ,1 ,-86 +146*w ,-405 +550*w ] , 11 + 8*w ); tzi([1 ,1 + w ,1 ,194 -304*w ,2111 -1142*w ] , 11 + 8*w ); tzi([ w , w , w ,0 ,0 ] , 13 + 6*w ); tzi([ w ,1 - w ,1 ,0 ,0 ] , 17 ); tzi([ w ,1 - w ,1 ,5*w ,-4 ] , 17 ); tzi([ w ,1 - w ,1 ,90*w ,-310 ] , 17 ); tzi([ w ,1 - w ,1 ,0 ,-14 ] , 17 ); tzi([1 ,0 ,1 ,1 ,2 ] , 10 + 10*w ); tzi([1 ,0 ,1 ,-19 ,26 ] , 10 + 10*w ); tzi([1 ,0 ,1 ,-14 ,-64 ] , 10 + 10*w ); tzi([1 ,0 ,1 ,-289 ,1862 ] , 10 + 10*w ); tzi([1 ,0 ,1 ,-69 ,-194 ] , 10 + 10*w ); tzi([1 ,0 ,1 ,-334 ,-2368 ] , 10 + 10*w ); tzi([1 ,0 ,1 ,-454 ,-544 ] , 10 + 10*w ); tzi([1 ,0 ,1 ,-5334 ,-150368 ] , 10 + 10*w ); tzi([1 + w ,0 ,1 ,-2 + w ,-1 ] , 18 ); tzi([1 + w ,0 ,1 ,-92 +61*w ,-289 +276*w ] , 18 ); tzi([1 + w ,0 ,1 ,-62 +91*w ,-13 -276*w ] , 18 ); tzi([1 ,-1 ,0 ,-3 ,3 ] , 18 ); tzi([1 + w ,0 ,1 ,13 -14*w ,29 ] , 18 ); tzi([1 + w ,1 + w ,1 + w ,10 -6*w ,1 -5*w ] , 14 + 7*w ); tzi([1 + w ,1 + w ,1 + w ,50 -21*w ,40 +109*w ] , 14 + 7*w ); tzi([1 + w ,1 + w , w ,-9 +11*w ,-14 +15*w ] , 14 + 7*w ); tzi([1 + w ,1 + w ,1 + w ,795 -331*w ,1413 +6644*w ] , 14 + 7*w ); tzi([1 + w ,1 + w ,1 + w ,-55 +49*w ,103 +410*w ] , 14 + 7*w ); tzi([1 + w ,1 + w , w ,-34 +51*w ,-41 -79*w ] , 14 + 7*w ); tzi([1 + w ,1 + w , w ,56 -44*w ,143 -540*w ] , 14 + 7*w ); tzi([1 + w ,1 + w , w ,-524 +786*w ,-433 -6694*w ] , 14 + 7*w ); tzi([0 , -w ,1 ,-1 + w ,0 ] , 19 ); tzi([0 , -w ,1 ,9 -9*w ,-15 ] , 19 ); tzi([0 , -w ,1 ,769 -769*w ,-8470 ] , 19 ); tzi([0 , -w ,1 ,-31 -99*w ,74 -498*w ] , 19 ); tzi([0 , -w ,1 ,99 +31*w ,-424 +498*w ] , 19 ); tzi([1 ,1 ,0 ,-11 ,0 ] , 11 + 11*w ); tzi([1 ,1 ,0 ,-146 ,621 ] , 11 + 11*w ); tzi([1 ,1 ,0 ,-6 ,-9 ] , 11 + 11*w ); tzi([1 ,1 ,0 ,44 ,55 ] , 11 + 11*w ); tzi([ w ,1 + w ,1 ,0 ,0 ] , 15 + 7*w ); tzi([1 + w ,-1 ,1 + w ,-4 ,-2 ] , 17 + 5*w ); tzi([1 + w ,-1 ,1 + w ,-9 ,9 -3*w ] , 17 + 5*w ); tzi([1 + w ,-1 ,1 + w ,-129 +15*w ,600 -141*w ] , 17 + 5*w ); tzi([1 + w ,-1 ,1 + w ,31 -15*w ,42 +3*w ] , 17 + 5*w ); tzi([1 + w ,-1 ,1 + w ,436 -285*w ,1581 +1812*w ] , 17 + 5*w ); tzi([1 + w ,-1 ,1 + w ,266 +15*w ,1075 -1962*w ] , 17 + 5*w ); tzi([0 ,-1 + w ,0 , w ,0 ] , 20 ); tzi([0 ,-1 + w ,0 ,-4*w ,4 ] , 20 ); tzi([0 ,-1 + w ,0 ,41*w ,-116 ] , 20 ); tzi([0 ,-1 + w ,0 ,36*w ,-140 ] , 20 ); tzi([ w ,1 - w , w ,0 ,0 ] , 18 + 4*w ); tzi([0 , -w , w ,-2*w ,-1 + w ] , 16 + 7*w ); tzi([0 , -w , w ,-140 +68*w ,-400 +400*w ] , 16 + 7*w ); tzi([1 ,-1 , w ,-3 +4*w ,1 -4*w ] , 21 ); tzi([1 ,-1 , w ,-18 +19*w ,-11 +29*w ] , 21 ); tzi([ w ,1 - w ,1 + w ,-4 +2*w ,-3 +3*w ] , 21 ); tzi([1 ,-1 , w ,-288 +304*w ,-920 +2189*w ] , 21 ); tzi([1 ,-1 , w ,12 -26*w ,-50 +161*w ] , 21 ); tzi([ w ,1 - w ,1 + w ,-19 +17*w ,18 -30*w ] , 21 ); tzi([ w ,1 - w ,1 + w ,26 -13*w ,111 -162*w ] , 21 ); tzi([ w ,1 - w ,1 + w ,-304 +287*w ,1269 -2190*w ] , 21 ); tzi([ w , w , w ,-2 +2*w ,-1 + w ] , 15 + 10*w ); tzi([ w , w , w ,-7 +2*w ,7 -4*w ] , 15 + 10*w ); tzi([ w , w , w ,-112 +27*w ,444 -194*w ] , 15 + 10*w ); tzi([ w , w , w ,18 -23*w ,62 -34*w ] , 15 + 10*w ); tzi([ w ,1 + w ,0 , w ,0 ] , 16 + 9*w ); tzi([ w ,1 + w ,0 ,-4*w ,5 -8*w ] , 16 + 9*w );