Canonical model in $\mathbb{P}^{ 6 }$ defined by 10 equations
| $ 0 $ | $=$ | $ x u - w v $ |
| $=$ | $x z - y t$ |
| $=$ | $y u - z u + t v$ |
| $=$ | $x t + y w - z w$ |
| $=$ | $\cdots$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ x^{8} y^{2} + 4 x^{7} z^{3} + x^{6} y^{4} - 2 x^{5} y^{2} z^{3} - 2 x^{3} y^{4} z^{3} + x^{2} y^{2} z^{6} + y^{4} z^{6} $ |
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This modular curve has 2 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 108 from the canonical model of this modular curve to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle -\frac{5}{2^5}\cdot\frac{12800000x^{9}+76800000x^{3}v^{6}+5524427372xwt^{3}v^{4}-3938996224xt^{8}-434875092xt^{2}v^{6}+10030980096yt^{6}v^{2}+806400000yv^{8}+1600000000z^{9}+960000000z^{7}v^{2}-1870250000z^{5}v^{4}-65118712000z^{3}v^{6}-38751543296zt^{6}v^{2}+2574599825zv^{8}+2779165328wt^{4}v^{4}+499265536t^{9}-5691190372t^{3}v^{6}+1249744tu^{8}-535141952tu^{5}v^{3}+2570675267tu^{2}v^{6}}{308xwt^{3}v^{4}+59904xt^{8}-1076xt^{2}v^{6}+37504yt^{6}v^{2}-950000z^{5}v^{4}-277000z^{3}v^{6}+65536zt^{6}v^{2}-2675zv^{8}-11408wt^{4}v^{4}-45056t^{9}-14196t^{3}v^{6}+176tu^{8}-2728tu^{5}v^{3}+3751tu^{2}v^{6}}$ |
Map
of degree 1 from the canonical model of this modular curve to the plane model of the modular curve
60.108.7.b.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle u$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle 2t$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle v$ |
Equation of the image curve:
| $0$ |
$=$ |
$ X^{8}Y^{2}+X^{6}Y^{4}+4X^{7}Z^{3}-2X^{5}Y^{2}Z^{3}-2X^{3}Y^{4}Z^{3}+X^{2}Y^{2}Z^{6}+Y^{4}Z^{6} $ |
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.
