Canonical model in $\mathbb{P}^{ 2 }$
| $ 0 $ | $=$ | $ 36 x^{4} - 2 x^{3} y - 10 x^{3} z + 3 x^{2} y^{2} + 12 x^{2} y z - 9 x^{2} z^{2} + 2 x y^{3} + \cdots - 2 y z^{3} $ |
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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 48 from the canonical model of this modular curve to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle \frac{2}{3^5}\cdot\frac{7569891574961144057x^{3}y^{9}+214170486773482356309x^{3}y^{8}z+2262795400192965657552x^{3}y^{7}z^{2}+11577026543969792504928x^{3}y^{6}z^{3}+30492261115024542612390x^{3}y^{5}z^{4}+38666978700395182390638x^{3}y^{4}z^{5}+12521515660582753100688x^{3}y^{3}z^{6}-21183822060044090496192x^{3}y^{2}z^{7}-21900102010318868921919x^{3}yz^{8}-5965846628616691949987x^{3}z^{9}-1324006436898968061x^{2}y^{10}-15816403732364733777x^{2}y^{9}z+46292174022950279427x^{2}y^{8}z^{2}+1518000797334050240268x^{2}y^{7}z^{3}+9117495964218868169844x^{2}y^{6}z^{4}+25771922786785248804594x^{2}y^{5}z^{5}+37429808606439164543424x^{2}y^{4}z^{6}+23336403813384900324348x^{2}y^{3}z^{7}-1945442480052172544223x^{2}y^{2}z^{8}-8633567312565110126265x^{2}yz^{9}-2679018789557156010219x^{2}z^{10}-1056978673107597386xy^{11}-27389337052749921260xy^{10}z-266967875185403684063xy^{9}z^{2}-1186559827226219696415xy^{8}z^{3}-1962820054777418567727xy^{7}z^{4}+2468784989093050434639xy^{6}z^{5}+14531759111862838369827xy^{5}z^{6}+20676704467440026300589xy^{4}z^{7}+10358452544716191768453xy^{3}z^{8}-1208008784183158942447xy^{2}z^{9}-2393477534783528333536xyz^{10}-455905232879886265426xz^{11}-144603922678272y^{12}-1055243426035458122y^{11}z-22911747067249553681y^{10}z^{2}-185055536785652564757y^{9}z^{3}-681023748118352594598y^{8}z^{4}-961535693329673171733y^{7}z^{5}+764213159467047482076y^{6}z^{6}+4040049090820497732807y^{5}z^{7}+4237099321032711069774y^{4}z^{8}+779380457812904915535y^{3}z^{9}-1082174024931209862379y^{2}z^{10}-455905230499574781010yz^{11}-198359290368z^{12}}{1502106754336x^{3}y^{9}-5875437034296x^{3}y^{8}z-65006034247872x^{3}y^{7}z^{2}-131769818450976x^{3}y^{6}z^{3}+422904476968632x^{3}y^{5}z^{4}-199662646762008x^{3}y^{4}z^{5}-176795078000784x^{3}y^{3}z^{6}+204262502702544x^{3}y^{2}z^{7}-71820504237672x^{3}yz^{8}+8789776359104x^{3}z^{9}+3421323684849x^{2}y^{10}+33588778743438x^{2}y^{9}z+46125195446517x^{2}y^{8}z^{2}-211355141928888x^{2}y^{7}z^{3}+20153407931430x^{2}y^{6}z^{4}+260061002820276x^{2}y^{5}z^{5}-142910859270018x^{2}y^{4}z^{6}-79814986941432x^{2}y^{3}z^{7}+98659044014649x^{2}y^{2}z^{8}-33428380114194x^{2}yz^{9}+3921028094493x^{2}z^{10}+860879001854xy^{11}+13538897472332xy^{10}z+45329860068578xy^{9}z^{2}-44373152174952xy^{8}z^{3}-116577056252442xy^{7}z^{4}+106060240973382xy^{6}z^{5}+82042609703166xy^{5}z^{6}-127897470396738xy^{4}z^{7}+45456970959396xy^{3}z^{8}+2385423491302xy^{2}z^{9}-4394403044360xyz^{10}+672721582738xz^{11}+860879001854y^{11}z+7534936781921y^{10}z^{2}+6067622799384y^{9}z^{3}-23767917919704y^{8}z^{4}-12715998731082y^{7}z^{5}+36615590758158y^{6}z^{6}+1006524619158y^{5}z^{7}-31112064567096y^{4}z^{8}+22001764461036y^{3}z^{9}-6292368630383y^{2}z^{10}+672721582738yz^{11}}$ |
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.
