Canonical model in $\mathbb{P}^{ 2 }$
| $ 0 $ | $=$ | $ 2 x^{4} - 4 x^{3} y + 4 x^{3} z + 6 x^{2} y^{2} + 17 x^{2} y z + 5 x^{2} z^{2} - 4 x y^{3} - 17 x y^{2} z + \cdots - 2 z^{4} $ |
![Copy content]()
![Toggle raw display]()
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
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle 2\cdot5^2\,\frac{2808x^{2}y^{13}+51880x^{2}y^{12}z+435274x^{2}y^{11}z^{2}+2365338x^{2}y^{10}z^{3}+9110190x^{2}y^{9}z^{4}+26111038x^{2}y^{8}z^{5}+56462820x^{2}y^{7}z^{6}+91565124x^{2}y^{6}z^{7}+109022548x^{2}y^{5}z^{8}+90187620x^{2}y^{4}z^{9}+48965042x^{2}y^{3}z^{10}+16482690x^{2}y^{2}z^{11}+3136806x^{2}yz^{12}+265302x^{2}z^{13}-2808xy^{14}-49072xy^{13}z-383394xy^{12}z^{2}-1930064xy^{11}z^{3}-6744852xy^{10}z^{4}-17000848xy^{9}z^{5}-30351782xy^{8}z^{6}-35102304xy^{7}z^{7}-17457424xy^{6}z^{8}+18834928xy^{5}z^{9}+41222578xy^{4}z^{10}+32482352xy^{3}z^{11}+13345884xy^{2}z^{12}+2871504xyz^{13}+265302xz^{14}+1728y^{15}+15952y^{14}z+90460y^{13}z^{2}+336519y^{12}z^{3}+884310y^{11}z^{4}+1667224y^{10}z^{5}+2104542y^{9}z^{6}+1573455y^{8}z^{7}-543716y^{7}z^{8}-3474120y^{6}z^{9}-7892872y^{5}z^{10}-11484267y^{4}z^{11}-9655250y^{3}z^{12}-4597344y^{2}z^{13}-1170450yz^{14}-132651z^{15}}{7x^{2}y^{13}+593x^{2}y^{12}z+11914x^{2}y^{11}z^{2}+92914x^{2}y^{10}z^{3}+353505x^{2}y^{9}z^{4}+731187x^{2}y^{8}z^{5}+850168x^{2}y^{7}z^{6}+549044x^{2}y^{6}z^{7}+196209x^{2}y^{5}z^{8}+45715x^{2}y^{4}z^{9}+6598x^{2}y^{3}z^{10}+642x^{2}y^{2}z^{11}+31x^{2}yz^{12}+x^{2}z^{13}-7xy^{14}-586xy^{13}z-11321xy^{12}z^{2}-81000xy^{11}z^{3}-260591xy^{10}z^{4}-377682xy^{9}z^{5}-118981xy^{8}z^{6}+301124xy^{7}z^{7}+352835xy^{6}z^{8}+150494xy^{5}z^{9}+39117xy^{4}z^{10}+5956xy^{3}z^{11}+611xy^{2}z^{12}+30xyz^{13}+xz^{14}+6y^{15}+341y^{14}z+3925y^{13}z^{2}+14416y^{12}z^{3}+19374y^{11}z^{4}+7451y^{10}z^{5}+4921y^{9}z^{6}-8160y^{8}z^{7}-73144y^{7}z^{8}-100901y^{6}z^{9}-52451y^{5}z^{10}-14656y^{4}z^{11}-2580y^{3}z^{12}-251y^{2}z^{13}-19yz^{14}}$ |
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.
