K:=NumberField(x^2+2); 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([ t ,1 - t ,1 ,-1 ,0 ] , 1 - 2*t ); tzi([0 ,0 ,0 ,1 ,0 ] , 4*t ); tzi([0 ,0 ,0 ,-1 ,0 ] , 4*t ); tzi([ t ,-1 , t ,-1 ,0 ] , 4*t ); tzi([ t ,-1 ,0 ,-2 ,3 ] , 4*t ); tzi([ t ,-1 + t ,1 , -t ,0 ] , 7 + t ); tzi([ t ,-1 + t ,1 + t ,2 -2*t ,0 ] , 7 + t ); tzi([1 + t ,0 ,1 ,-1 - t ,0 ] , 2 + 5*t ); tzi([1 ,1 - t ,0 ,-1 - t ,-1 ] , 2 + 5*t ); tzi([1 ,1 - t ,0 ,4 -11*t ,-26 ] , 2 + 5*t ); tzi([1 ,1 - t ,0 ,69 -51*t ,339 +62*t ] , 2 + 5*t ); tzi([ t ,1 , t ,0 ,0 ] , 6*t ); tzi([ t ,1 , t ,-15 ,-27 ] , 6*t ); tzi([ t ,1 , t ,-5 ,5 ] , 6*t ); tzi([0 ,-1 ,0 ,1 ,0 ] , 6*t ); tzi([ t ,1 , t ,-95 ,347 ] , 6*t ); tzi([ t ,1 , t ,5 ,23 ] , 6*t ); tzi([ t ,1 , t ,85 +70*t ,559 -98*t ] , 6*t ); tzi([ t ,1 , t ,85 -70*t ,559 +98*t ] , 6*t ); tzi([1 ,0 ,1 ,-1 ,0 ] , 7*t ); tzi([1 ,0 ,1 ,-11 ,12 ] , 7*t ); tzi([1 ,0 ,1 ,4 ,-6 ] , 7*t ); tzi([1 ,0 ,1 ,-36 ,-70 ] , 7*t ); tzi([1 ,0 ,1 ,-171 ,-874 ] , 7*t ); tzi([1 ,0 ,1 ,-2731 ,-55146 ] , 7*t ); tzi([1 + t ,1 - t ,1 + t ,-2*t , -t ] , 9 + 3*t ); tzi([1 + t ,1 - t ,1 + t ,-5 -2*t ,4 + t ] , 9 + 3*t ); tzi([1 + t ,1 - t ,1 + t ,-90 -12*t ,302 +71*t ] , 9 + 3*t ); tzi([1 + t ,1 - t ,1 + t ,8*t ,22 +19*t ] , 9 + 3*t ); tzi([1 + t ,1 - t ,1 + t ,-15 +173*t ,1006 +859*t ] , 9 + 3*t ); tzi([1 + t ,1 - t ,1 + t ,95 +3*t ,-30 +251*t ] , 9 + 3*t ); tzi([0 ,1 ,0 ,-1 ,0 ] , 10 ); tzi([ t ,0 , t ,2 ,0 ] , 10 ); tzi([0 ,1 ,0 ,-41 ,-116 ] , 10 ); tzi([ t ,0 , t ,-8 ,18 ] , 10 ); tzi([ t ,1 - t , t ,4 -3*t ,4 -2*t ] , 6 + 6*t ); tzi([ t ,1 - t , t ,49 -48*t ,265 +7*t ] , 6 + 6*t ); tzi([0 ,-1 - t ,0 ,9 ,-2 +5*t ] , 6 + 6*t ); tzi([ t ,1 - t , t ,-21 +2*t ,37 +13*t ] , 6 + 6*t ); tzi([ t ,1 - t ,0 ,-1 -4*t ,-7 + t ] , 6 + 6*t ); tzi([ t ,1 - t ,0 ,14 +11*t ,-19 +16*t ] , 6 + 6*t ); tzi([0 ,-1 - t ,0 ,-7 -4*t ,4 +11*t ] , 6 + 6*t ); tzi([ t ,1 - t ,0 ,4 -59*t ,-261 +122*t ] , 6 + 6*t ); tzi([1 , -t , t , -t ,0 ] , 4 + 7*t ); tzi([1 , -t , t ,10 - t ,2 +6*t ] , 4 + 7*t ); tzi([1 , -t , t ,170 -6*t ,68 +549*t ] , 4 + 7*t ); tzi([1 , -t , t ,10 +4*t ,24 +7*t ] , 4 + 7*t ); tzi([0 ,-1 ,1 ,0 ,0 ] , 11 ); tzi([0 ,-1 ,1 ,-10 ,-20 ] , 11 ); tzi([0 ,-1 ,1 ,-7820 ,-263580 ] , 11 ); tzi([ t ,1 ,1 ,3 -3*t ,-3 - t ] , 7 - 6*t ); tzi([ t ,0 , t ,0 ,1 ] , 12 ); tzi([ t ,0 , t ,-15 ,28 ] , 12 ); tzi([ t ,0 , t ,-5 ,-4 ] , 12 ); tzi([0 ,1 ,0 ,1 ,0 ] , 12 ); tzi([ t ,0 , t ,-95 ,-346 ] , 12 ); tzi([ t ,0 , t ,5 ,-22 ] , 12 ); tzi([ t ,0 , t ,85 -70*t ,-558 -98*t ] , 12 ); tzi([ t ,0 , t ,85 +70*t ,-558 +98*t ] , 12 ); tzi([ t ,1 - t , t ,2 ,1 - t ] , 6 + 8*t ); tzi([0 ,-1 - t ,0 ,1 +2*t ,2 - t ] , 6 + 8*t ); tzi([1 + t ,-1 + t ,1 ,-2 -2*t ,1 ] , 4 + 9*t ); tzi([1 + t ,-1 + t ,1 ,8 -17*t ,55 +6*t ] , 4 + 9*t ); tzi([1 , t ,1 ,-1 ,0 ] , 12 + 5*t ); tzi([1 ,1 - t , t ,2 ,2 -2*t ] , 10 + 7*t ); tzi([1 ,1 - t , t ,42 +10*t ,86 -80*t ] , 10 + 7*t ); tzi([1 + t ,0 ,1 + t ,1 + t ,2 + t ] , 10 + 7*t ); tzi([1 + t ,0 ,1 + t ,-19 -4*t ,38 + t ] , 10 + 7*t ); tzi([0 ,0 ,0 ,-2 ,1 ] , 10*t ); tzi([ t ,-1 , t ,0 ,2 ] , 10*t ); tzi([ t ,-1 , t ,-25 ,67 ] , 10*t ); tzi([ t ,-1 , t ,5 ,3 ] , 10*t ); tzi([ t , t ,1 + t , t ,0 ] , 11 + 7*t ); tzi([ t , t ,1 + t , -t , -t ] , 11 + 7*t ); tzi([1 ,1 ,1 ,0 ,0 ] , 15 ); tzi([1 ,1 ,1 ,-5 ,2 ] , 15 ); tzi([1 ,1 ,1 ,-80 ,242 ] , 15 ); tzi([1 ,1 ,1 ,-10 ,-10 ] , 15 ); tzi([1 ,1 ,1 ,-135 ,-660 ] , 15 ); tzi([1 ,1 ,1 ,35 ,-28 ] , 15 ); tzi([1 ,1 ,1 ,-2160 ,-39540 ] , 15 ); tzi([1 ,1 ,1 ,-110 ,-880 ] , 15 ); tzi([ t ,-1 ,1 + t ,2 -3*t ,5 - t ] , 5 + 10*t ); tzi([ t ,-1 ,1 ,8 +2*t ,-9 +4*t ] , 5 + 10*t ); tzi([1 + t , t ,1 ,13 +9*t ,40 +10*t ] , 12 + 7*t ); tzi([1 ,1 ,0 ,-194 -35*t ,938 +268*t ] , 12 + 7*t ); tzi([1 ,1 , t ,-41 +7*t ,-121 +29*t ] , 12 + 7*t ); tzi([1 + t , t ,1 ,-13 -41*t ,122 -109*t ] , 12 + 7*t ); tzi([1 + t , -t ,1 + t ,-3*t ,0 ] , 2 + 11*t ); tzi([1 ,-1 + t ,1 ,-1 + t ,-2 - t ] , 7 + 10*t ); tzi([0 , t ,0 ,1 , t ] , 16 ); tzi([0 , -t ,0 ,1 , -t ] , 16 ); tzi([0 ,-1 ,0 ,-2 ,2 ] , 16 ); tzi([0 ,-1 ,0 ,1 ,-1 ] , 16 ); tzi([0 ,1 ,0 ,-2 ,-2 ] , 16 ); tzi([0 ,1 ,0 ,1 ,1 ] , 16 ); tzi([1 + t , t ,0 , -t ,0 ] , 16 + t ); tzi([1 + t , t ,0 ,4*t ,-12 - t ] , 16 + t ); tzi([ t ,1 , t ,-1 -2*t ,-1 -2*t ] , 16 + 2*t ); tzi([ t ,1 , t ,-1 +8*t ,-1 -12*t ] , 16 + 2*t ); tzi([ t ,0 ,1 + t ,-2*t ,-1 -3*t ] , 5 + 11*t ); tzi([ t ,0 ,1 + t ,8 -4*t ,7 +4*t ] , 5 + 11*t ); tzi([ t ,0 ,1 + t ,-170 -157*t ,-332 -1222*t ] , 5 + 11*t ); tzi([ t ,0 ,1 + t ,-42 -39*t ,48 +165*t ] , 5 + 11*t ); tzi([0 ,1 ,0 ,-2 ,0 ] , 12*t ); tzi([ t ,0 , t ,-7 ,-7 ] , 12*t ); tzi([0 ,1 ,0 ,-4 ,2 ] , 12*t ); tzi([ t ,0 ,0 ,2 ,-1 ] , 12*t ); tzi([ t ,0 ,0 ,22 +5*t ,-23 +26*t ] , 12*t ); tzi([ t ,0 ,0 ,22 -5*t ,-23 -26*t ] , 12*t ); tzi([0 ,-1 ,0 ,-2 ,0 ] , 12*t ); tzi([ t ,1 , t ,-7 ,8 ] , 12*t ); tzi([0 ,-1 ,0 ,-4 ,-2 ] , 12*t ); tzi([ t ,1 ,0 ,2 ,1 ] , 12*t ); tzi([ t ,1 ,0 ,22 +5*t ,23 -26*t ] , 12*t ); tzi([ t ,1 ,0 ,22 -5*t ,23 +26*t ] , 12*t ); tzi([0 , t ,0 ,1 ,3*t ] , 12*t ); tzi([0 , t ,0 ,11 ,-7*t ] , 12*t ); tzi([ t ,-1 + t ,0 ,-2 +4*t ,-5 -8*t ] , 12*t ); tzi([ t ,-1 + t , t ,-1 -6*t ,8 -3*t ] , 12*t ); tzi([ t ,-1 + t ,0 ,-32 +79*t ,-215 -374*t ] , 12*t ); tzi([ t ,-1 + t ,0 ,-12 +9*t ,-15 +6*t ] , 12*t ); tzi([ t ,-1 + t , t ,-31 -81*t ,248 -294*t ] , 12*t ); tzi([ t ,-1 + t , t ,-11 -11*t ,28 +16*t ] , 12*t ); tzi([0 , -t ,0 ,1 ,-3*t ] , 12*t ); tzi([0 , -t ,0 ,11 ,7*t ] , 12*t ); tzi([ t ,-1 - t , t ,-1 +6*t ,8 +3*t ] , 12*t ); tzi([ t ,-1 - t ,0 ,-2 -4*t ,-5 +8*t ] , 12*t ); tzi([ t ,-1 - t , t ,-31 +81*t ,248 +294*t ] , 12*t ); tzi([ t ,-1 - t , t ,-11 +11*t ,28 -16*t ] , 12*t ); tzi([ t ,-1 - t ,0 ,-32 -79*t ,-215 +374*t ] , 12*t ); tzi([ t ,-1 - t ,0 ,-12 -9*t ,-15 -6*t ] , 12*t ); tzi([1 ,-1 ,1 ,-1 ,0 ] , 17 ); tzi([1 ,-1 ,1 ,-6 ,-4 ] , 17 ); tzi([1 ,-1 ,1 ,-91 ,-310 ] , 17 ); tzi([1 ,-1 ,1 ,-1 ,-14 ] , 17 ); tzi([ t ,1 - t ,1 + t ,-1 - t ,1 ] , 15 + 6*t ); tzi([ t ,1 - t ,1 + t ,1 + t , -t ] , 15 + 6*t ); tzi([ t ,1 - t ,1 + t ,-1 -46*t ,104 -109*t ] , 15 + 6*t ); tzi([ t ,1 - t ,1 + t ,1 -14*t ,-17 +7*t ] , 15 + 6*t ); tzi([0 ,-1 + t ,1 ,1 - t , t ] , 13 + 8*t ); tzi([0 ,-1 + t ,1 ,11 -11*t ,-27 +3*t ] , 13 + 8*t ); tzi([0 ,-1 + t ,1 ,-9 +39*t ,-210 -39*t ] , 13 + 8*t ); tzi([0 ,1 - t ,1 ,2 -2*t ,1 ] , 13 + 8*t ); tzi([ t ,1 - t ,1 + t ,-3*t ,1 -2*t ] , 3 + 12*t ); tzi([ t ,1 - t ,1 ,-6 -2*t ,-7 ] , 3 + 12*t );