Canonical model in $\mathbb{P}^{ 2 }$
$ 0 $ | $=$ | $ x^{3} z + x^{2} y^{2} - x y z^{2} - y^{3} z + 5 z^{4} $ |
This modular curve has 4 rational cusps but no known non-cuspidal rational points. The following are the coordinates of the rational cusps on this modular curve.
Maps to other modular curves
$j$-invariant map
of degree 72 from the canonical model of this modular curve to the modular curve
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle -\frac{x^{18}-714x^{16}yz-174951x^{15}z^{3}+15875374x^{13}yz^{4}+294242376x^{12}z^{6}-2231220361x^{10}yz^{7}-6838076244x^{9}z^{9}+9461848986x^{7}yz^{10}-31494996496x^{6}z^{12}+14122661253x^{4}yz^{13}+23950271597x^{3}z^{15}-93750xy^{16}z+1468750xy^{13}z^{4}+1890625xy^{10}z^{7}+19940202xy^{7}z^{10}-3299371917xy^{4}z^{13}+11703100608xyz^{16}+15625y^{18}-140625y^{15}z^{3}-375000y^{12}z^{6}-55952412y^{9}z^{9}+2642480720y^{6}z^{12}-29288460677y^{3}z^{15}+86629783010z^{18}}{z(x^{16}y-30x^{15}z^{2}-391x^{13}yz^{3}+2741x^{12}z^{5}+11197x^{10}yz^{6}-8654x^{9}z^{8}+82705x^{7}yz^{9}-542666x^{6}z^{11}-1177994x^{4}yz^{12}-4357560x^{3}z^{14}-15625xy^{10}z^{6}-15204xy^{7}z^{9}+1538129xy^{4}z^{12}-5301770xyz^{15}+93749y^{9}z^{8}-1092023y^{6}z^{11}+5501185y^{3}z^{14}-11104775z^{17})}$ |
The following modular covers realize this modular curve as a fiber product over $X(1)$.
This modular curve minimally covers the modular curves listed below.
This modular curve is minimally covered by the modular curves in the database listed below.