
//// Genus 0 with rational points:
 Genus0_P1 := [
["4X3","3B"],
["4X3","5S4"],
["4X3","7B"],
["4X7","3Nn"],
["8X4","3B"],
["8X4","5S4"],
["8X4","7B"],
["8X5","3B"],
["8X5","5S4"],
["8X5","7B"]
];

//// Genus 0 without rational points:
 Genus0_PointlessConic := [
];

//// j-maps of Genus 0 curves:
 Genus0_jmaps := <
<["4X3","3B"],(-9*t^8 + 72*t^7 + 504*t^6 - 4032*t^5 - 11160*t^4 + 72864*t^3 + 116064*t^2 - 389376*t - 316368)/(t^6 - 6*t^5 + 15*t^4 - 20*t^3 + 15*t^2 - 6*t + 1),(3*t^4 - 12*t^3 + 180*t^2 - 336*t - 564)/(t^3 - 3*t^2 + 3*t - 1)>,
<["4X3","5S4"],(1728*t^10 - 2025*t^8 + 900*t^6 - 190*t^4 + 20*t^2 - 1)/t^10,(45*t^4 - 10*t^2 + 1)/t^5>,
<["4X3","7B"],(-t^16 + 748*t^14 - 196882*t^12 + 20706224*t^10 - 695893835*t^8 + 10976181104*t^6 - 90957030178*t^4 + 387556041628*t^2 - 678223072849)/t^14,(-t^8 - 490*t^6 + 21609*t^4 - 235298*t^2 + 823543)/t^7>,
<["4X7","3Nn"],(-512*t^9 - 48*t^6 - 3/2*t^3 - 1/64)/t^12,(-8*t^3 - 1/4)/t^3>,
<["8X4","3B"],(-9/2*t^8 + 36*t^7 + 630*t^6 - 4284*t^5 - 32715*t^4 + 160092*t^3 + 693558*t^2 - 1719108*t - 6699465/2)/(t^6 - 6*t^5 + 15*t^4 - 20*t^3 + 15*t^2 - 6*t + 1),(3/2*t^4 - 6*t^3 + 171*t^2 - 330*t - 2589/2)/(t^3 - 3*t^2 + 3*t - 1)>,
<["8X4","5S4"],(1728*t^10 - 4050*t^8 + 3600*t^6 - 1520*t^4 + 320*t^2 - 32)/t^10,(45*t^4 - 20*t^2 + 4)/t^5>,
<["8X4","7B"],(-678223072849/128*t^16 + 96889010407/16*t^14 - 45478515089/16*t^12 + 686011319*t^10 - 695893835/8*t^8 + 5176556*t^6 - 98441*t^4 + 748*t^2 - 2)/t^2,(-823543/16*t^8 + 117649/4*t^6 - 21609/4*t^4 + 245*t^2 + 1)/t>,
<["8X5","3B"],(9/2*t^8 + 756*t^6 + 43740*t^4 + 944784*t^2 + 4251528)/t^6,(3/2*t^4 - 162*t^2 - 1458)/t^3>,
<["8X5","5S4"],(1728*t^10 + 4050*t^8 + 3600*t^6 + 1520*t^4 + 320*t^2 + 32)/t^10,(45*t^4 + 20*t^2 + 4)/t^5>,
<["8X5","7B"],(678223072849/128*t^16 + 96889010407/16*t^14 + 45478515089/16*t^12 + 686011319*t^10 + 695893835/8*t^8 + 5176556*t^6 + 98441*t^4 + 748*t^2 + 2)/t^2,(-823543/16*t^8 - 117649/4*t^6 - 21609/4*t^4 - 245*t^2 + 1)/t>
>;
