F:= 7398655171875*t^17+148206064500*t^16+19150282563282*t^15+148206064500*t^14+ 7398655171875*t^13+(-14797310343750*t^17-119193616104750*t^16-174205118875788* t^15-174205118875788*t^14-119193616104750*t^13-14797310343750*t^12)*y+( 262272331913625*t^16+1523462955401628*t^15+1667862195882390*t^14+ 1523462955401628*t^13+262272331913625*t^12)*y^2+(-36543753774000*t^16-\ 3375884975416560*t^15-10559125325510496*t^14-10559125325510496*t^13-\ 3375884975416560*t^12-36543753774000*t^11)*y^3+(23379979887000*t^16+ 1879622008160220*t^15+24381595835814456*t^14+52217459762534568*t^13+ 24381595835814456*t^12+1879622008160220*t^11+23379979887000*t^10)*y^4+(-\ 6848226000000*t^16-1151935832250504*t^15-20294095830649704*t^14-\ 125248437685460880*t^13-125248437685460880*t^12-20294095830649704*t^11-\ 1151935832250504*t^10-6848226000000*t^9)*y^5+(3480246000000*t^16+ 371649738980016*t^15+14387154978990388*t^14+140547176465298176*t^13+ 325086786630360888*t^12+140547176465298176*t^11+14387154978990388*t^10+ 371649738980016*t^9+3480246000000*t^8)*y^6+(-1026432000000*t^16-\ 134738240796576*t^15-6282202563271536*t^14-128059694064775152*t^13-\ 410412946832497920*t^12-410412946832497920*t^11-128059694064775152*t^10-\ 6282202563271536*t^9-134738240796576*t^8-1026432000000*t^7)*y^7+(256608000000* t^16+21383144640000*t^15+2862276345300840*t^14+82971785546524938*t^13+ 428565125897695536*t^12+469607517282365628*t^11+428565125897695536*t^10+ 82971785546524938*t^9+2862276345300840*t^8+21383144640000*t^7+256608000000*t^6 )*y^8+(-7240337280000*t^15-991484631806336*t^14-46287895378500868*t^13-\ 336874615686463476*t^12-448310526391887240*t^11-448310526391887240*t^10-\ 336874615686463476*t^9-46287895378500868*t^8-991484631806336*t^7-7240337280000 *t^6)*y^9+(1219401216000*t^15+465330532949376*t^14+17684786413194144*t^13+ 241265088714763806*t^12+266089870836016872*t^11+447436580570407860*t^10+ 266089870836016872*t^9+241265088714763806*t^8+17684786413194144*t^7+ 465330532949376*t^6+1219401216000*t^5)*y^10+(-221709312000*t^15-\ 167460763987968*t^14-5360117987008704*t^13-136076799330833808*t^12-\ 150557853627476688*t^11-252728154714722016*t^10-252728154714722016*t^9-\ 150557853627476688*t^8-136076799330833808*t^7-5360117987008704*t^6-\ 167460763987968*t^5-221709312000*t^4)*y^11+(48524215742464*t^14+ 1301038919151104*t^13+69551430270896616*t^12+26807516850723084*t^11+ 225938746267906728*t^10-11588803559941944*t^9+225938746267906728*t^8+ 26807516850723084*t^7+69551430270896616*t^6+1301038919151104*t^5+ 48524215742464*t^4)*y^12+(-9386285432832*t^14-400838873938944*t^13-\ 33335590161232128*t^12+26331280164507192*t^11-138987204138618024*t^10-\ 299578279646352*t^9-299578279646352*t^8-138987204138618024*t^7+ 26331280164507192*t^6-33335590161232128*t^5-400838873938944*t^4-9386285432832* t^3)*y^13+(1340897918976*t^14+82382081937408*t^13+15440782735493376*t^12-\ 31301371764970320*t^11+74374424464699140*t^10-17686092769029696*t^9+ 22963724118160152*t^8-17686092769029696*t^7+74374424464699140*t^6-\ 31301371764970320*t^5+15440782735493376*t^4+82382081937408*t^3+1340897918976*t ^2)*y^14+(-12235782316032*t^13-5654355450974208*t^12+15001060138007392*t^11-\ 25190987918726992*t^10+4279227499180464*t^9-2394262539871680*t^8-\ 2394262539871680*t^7+4279227499180464*t^6-25190987918726992*t^5+ 15001060138007392*t^4-5654355450974208*t^3-12235782316032*t^2)*y^15+( 1589958132922368*t^12-5503911731463168*t^11+11315640618091032*t^10-\ 15437455816608789*t^9+25955998481173884*t^8-30601126597717758*t^7+ 25955998481173884*t^6-15437455816608789*t^5+11315640618091032*t^4-\ 5503911731463168*t^3+1589958132922368*t^2)*y^16+(-308196045324288*t^12+ 1374371911231488*t^11-3435929778078720*t^10+5676742872485274*t^9-\ 6722439283219662*t^8+3107254277581620*t^7+3107254277581620*t^6-\ 6722439283219662*t^5+5676742872485274*t^4-3435929778078720*t^3+ 1374371911231488*t^2-308196045324288*t)*y^17+(34244005036032*t^12-\ 205464030216192*t^11+671928195778560*t^10-1476220701911040*t^9+ 2375372767218961*t^8-2904271189787716*t^7+3043065912798822*t^6-\ 2904271189787716*t^5+2375372767218961*t^4-1476220701911040*t^3+671928195778560 *t^2-205464030216192*t+34244005036032)*y^18: # One obtains the following new relation: rel := Y^2-(X^2+X+7)*X; # and can express t,y in terms of X,Y as follows: t = 1/2-1/432*(X^9-84*X^6-378*X^5-1512*X^4-5208*X^3-7236*X^2-8127*X-784) /X/(X+1)^2/(X^2+X+7)^2*Y; y = 1/2-1/4*(3*X^8-2*X^7-4*X^6-204*X^5-536*X^4-1738*X^3-5064*X^2-4808*X-3199) /(X^6+196*X^3+189*X^2+756*X+154)/(X^2+X+7)/(X+1)*Y;