Canonical model in $\mathbb{P}^{ 2 }$
| $ 0 $ | $=$ | $ 2 x^{4} - 3 x^{3} y + 3 x^{3} z - 5 x^{2} y^{2} - 18 x^{2} y z - 5 x^{2} z^{2} - 4 x y^{3} - 17 x y^{2} z + \cdots - 2 z^{4} $ |
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This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Maps to other modular curves
$j$-invariant map
of degree 60 from the canonical model of this modular curve to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle 5^2\,\frac{942686181x^{3}y^{12}+7521205212x^{3}y^{11}z+21841462746x^{3}y^{10}z^{2}+26279261420x^{3}y^{9}z^{3}+8553933195x^{3}y^{8}z^{4}-3838235848x^{3}y^{7}z^{5}-2749142676x^{3}y^{6}z^{6}-3838235848x^{3}y^{5}z^{7}+8553933195x^{3}y^{4}z^{8}+26279261420x^{3}y^{3}z^{9}+21841462746x^{3}y^{2}z^{10}+7521205212x^{3}yz^{11}+942686181x^{3}z^{12}+1161438453x^{2}y^{13}+12366492993x^{2}y^{12}z+50057826552x^{2}y^{11}z^{2}+93833940112x^{2}y^{10}z^{3}+74146673325x^{2}y^{9}z^{4}+6215553441x^{2}y^{8}z^{5}-10741951784x^{2}y^{7}z^{6}+10741951784x^{2}y^{6}z^{7}-6215553441x^{2}y^{5}z^{8}-74146673325x^{2}y^{4}z^{9}-93833940112x^{2}y^{3}z^{10}-50057826552x^{2}y^{2}z^{11}-12366492993x^{2}yz^{12}-1161438453x^{2}z^{13}+816387768xy^{14}+8576491653xy^{13}z+32274478260xy^{12}z^{2}+46701809818xy^{11}z^{3}-1555516012xy^{10}z^{4}-60480360469xy^{9}z^{5}-28296834304xy^{8}z^{6}+12444669420xy^{7}z^{7}-28296834304xy^{6}z^{8}-60480360469xy^{5}z^{9}-1555516012xy^{4}z^{10}+46701809818xy^{3}z^{11}+32274478260xy^{2}z^{12}+8576491653xyz^{13}+816387768xz^{14}+345044610y^{15}+1836929070y^{14}z+2535309000y^{13}z^{2}+365319900y^{12}z^{3}+2866112280y^{11}z^{4}+6122843860y^{10}z^{5}-713164710y^{9}z^{6}-1091471650y^{8}z^{7}+1091471650y^{7}z^{8}+713164710y^{6}z^{9}-6122843860y^{5}z^{10}-2866112280y^{4}z^{11}-365319900y^{3}z^{12}-2535309000y^{2}z^{13}-1836929070yz^{14}-345044610z^{15}}{436429x^{3}y^{12}-32512x^{3}y^{11}z-2136286x^{3}y^{10}z^{2}+3087680x^{3}y^{9}z^{3}-598845x^{3}y^{8}z^{4}-3040832x^{3}y^{7}z^{5}+4626076x^{3}y^{6}z^{6}-3040832x^{3}y^{5}z^{7}-598845x^{3}y^{4}z^{8}+3087680x^{3}y^{3}z^{9}-2136286x^{3}y^{2}z^{10}-32512x^{3}yz^{11}+436429x^{3}z^{12}+537693x^{2}y^{13}+1395853x^{2}y^{12}z-3482508x^{2}y^{11}z^{2}-2075228x^{2}y^{10}z^{3}+11077825x^{2}y^{9}z^{4}-13186479x^{2}y^{8}z^{5}+10001136x^{2}y^{7}z^{6}-10001136x^{2}y^{6}z^{7}+13186479x^{2}y^{5}z^{8}-11077825x^{2}y^{4}z^{9}+2075228x^{2}y^{3}z^{10}+3482508x^{2}y^{2}z^{11}-1395853x^{2}yz^{12}-537693x^{2}z^{13}+377976xy^{14}+927181xy^{13}z-3365160xy^{12}z^{2}-1424414xy^{11}z^{3}+12384616xy^{10}z^{4}-15132733xy^{9}z^{5}+6603592xy^{8}z^{6}-738020xy^{7}z^{7}+6603592xy^{6}z^{8}-15132733xy^{5}z^{9}+12384616xy^{4}z^{10}-1424414xy^{3}z^{11}-3365160xy^{2}z^{12}+927181xyz^{13}+377976xz^{14}+159762y^{15}-436218y^{14}z+105520y^{13}z^{2}+1873220y^{12}z^{3}-5294352y^{11}z^{4}+8188412y^{10}z^{5}-8953166y^{9}z^{6}+8392350y^{8}z^{7}-8392350y^{7}z^{8}+8953166y^{6}z^{9}-8188412y^{5}z^{10}+5294352y^{4}z^{11}-1873220y^{3}z^{12}-105520y^{2}z^{13}+436218yz^{14}-159762z^{15}}$ |
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.
