Canonical model in $\mathbb{P}^{ 2 }$
| $ 0 $ | $=$ | $ x^{4} + 9 x^{2} y^{2} - x^{2} y z - 14 x^{2} z^{2} + 14 y^{4} + 8 y^{3} z - 19 y^{2} z^{2} + 7 y z^{3} - 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
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle -5^2\,\frac{(y-z)(132587x^{2}y^{12}+288007x^{2}y^{11}z-1142917x^{2}y^{10}z^{2}-3519245x^{2}y^{9}z^{3}+1299265x^{2}y^{8}z^{4}+11909897x^{2}y^{7}z^{5}+6427877x^{2}y^{6}z^{6}-13487547x^{2}y^{5}z^{7}-14301360x^{2}y^{4}z^{8}+2086620x^{2}y^{3}z^{9}+7177908x^{2}y^{2}z^{10}+2896668x^{2}yz^{11}+363312x^{2}z^{12}+264854y^{14}+837988y^{13}z-1332539y^{12}z^{2}-7229793y^{11}z^{3}-2723141y^{10}z^{4}+16717019y^{9}z^{5}+15896893y^{8}z^{6}-12487479y^{7}z^{7}-17628773y^{6}z^{8}+1971049y^{5}z^{9}+5384146y^{4}z^{10}+314212y^{3}z^{11}-427736y^{2}z^{12}+24268yz^{13}+25816z^{14})}{5x^{2}y^{12}z-70x^{2}y^{11}z^{2}+420x^{2}y^{10}z^{3}-1175x^{2}y^{9}z^{4}+100x^{2}y^{8}z^{5}+7905x^{2}y^{7}z^{6}-13020x^{2}y^{6}z^{7}-17155x^{2}y^{5}z^{8}+49600x^{2}y^{4}z^{9}+16425x^{2}y^{3}z^{10}-73830x^{2}y^{2}z^{11}-6930x^{2}yz^{12}+39005x^{2}z^{13}+y^{15}+5y^{14}z-135y^{13}z^{2}+750y^{12}z^{3}-1655y^{11}z^{4}-1511y^{10}z^{5}+15580y^{9}z^{6}-16785y^{8}z^{7}-42850y^{7}z^{8}+76745y^{6}z^{9}+48882y^{5}z^{10}-111555y^{4}z^{11}-6140y^{3}z^{12}+53075y^{2}z^{13}-19995yz^{14}+2772z^{15}}$ |
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.
