Canonical model in $\mathbb{P}^{ 9 }$ defined by 28 equations
| $ 0 $ | $=$ | $ t v - t a + u s $ |
| $=$ | $t s - u v - u s - v r$ |
| $=$ | $t v + t a + u v - u s + u a - r s$ |
| $=$ | $y t + y u + z s - w t - w u$ |
| $=$ | $\cdots$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 198470250000 x^{16} y - 396940500000 x^{16} z + 54456300000 x^{14} y^{3} + 3530501437500 x^{14} y^{2} z + \cdots + 69564732336 z^{17} $ |
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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
Map
of degree 3 from the canonical model of this modular curve to the canonical model of the modular curve
60.60.4.p.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle -y$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle -z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle 2t-3u-r$ |
| $\displaystyle W$ |
$=$ |
$\displaystyle -v-3s+a$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 15X^{2}+105Y^{2}+Z^{2}-W^{2} $ |
|
$=$ |
$ 15X^{2}Y-15Y^{3}+YZ^{2}-XZW $ |
Map
of degree 1 from the canonical model of this modular curve to the plane model of the modular curve
60.180.10.x.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle w$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle -4r+4a$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle s$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 198470250000X^{16}Y+54456300000X^{14}Y^{3}+5780970000X^{12}Y^{5}+292086000X^{10}Y^{7}+6804000X^{8}Y^{9}+54000X^{6}Y^{11}-396940500000X^{16}Z+3530501437500X^{14}Y^{2}Z+270535545000X^{12}Y^{4}Z+3067753500X^{10}Y^{6}Z-51507900X^{8}Y^{8}Z-1074600X^{6}Y^{10}Z+900X^{4}Y^{12}Z+43793690850000X^{14}YZ^{2}-919263532500X^{12}Y^{3}Z^{2}-109145880000X^{10}Y^{5}Z^{2}-1278244800X^{8}Y^{7}Z^{2}-10886400X^{6}Y^{9}Z^{2}-75600X^{4}Y^{11}Z^{2}-102118575150000X^{14}Z^{3}-50345966542500X^{12}Y^{2}Z^{3}-469498872375X^{10}Y^{4}Z^{3}+4042896300X^{8}Y^{6}Z^{3}+251314380X^{6}Y^{8}Z^{3}+862920X^{4}Y^{10}Z^{3}-1080X^{2}Y^{12}Z^{3}+230181903090000X^{12}YZ^{4}+18799331472000X^{10}Y^{3}Z^{4}+212403870000X^{8}Y^{5}Z^{4}+758989440X^{6}Y^{7}Z^{4}+11160000X^{4}Y^{9}Z^{4}+26640X^{2}Y^{11}Z^{4}-248321347650000X^{12}Z^{5}-81747506920500X^{10}Y^{2}Z^{5}-1197310497075X^{8}Y^{4}Z^{5}-19624015800X^{6}Y^{6}Z^{5}-205890084X^{4}Y^{8}Z^{5}-55416X^{2}Y^{10}Z^{5}+324Y^{12}Z^{5}+78959507778000X^{10}YZ^{6}-11669588586900X^{8}Y^{3}Z^{6}-53320446720X^{6}Y^{5}Z^{6}-192795552X^{4}Y^{7}Z^{6}-3667200X^{2}Y^{9}Z^{6}-432Y^{11}Z^{6}+35565712794000X^{10}Z^{7}+104474294772300X^{8}Y^{2}Z^{7}+1303427616570X^{6}Y^{4}Z^{7}+14068889640X^{4}Y^{6}Z^{7}+41931876X^{2}Y^{8}Z^{7}-36072Y^{10}Z^{7}-258066667731600X^{8}YZ^{8}-989040862080X^{6}Y^{3}Z^{8}-32975935632X^{4}Y^{5}Z^{8}+28518288X^{2}Y^{7}Z^{8}+45600Y^{9}Z^{8}+199546786753200X^{8}Z^{9}-31682811046860X^{6}Y^{2}Z^{9}-392163634206X^{4}Y^{4}Z^{9}-2682701412X^{2}Y^{6}Z^{9}+966160Y^{8}Z^{9}+115869864599280X^{6}YZ^{10}+1807871776452X^{4}Y^{3}Z^{10}+10723982784X^{2}Y^{5}Z^{10}+3180128Y^{7}Z^{10}-116694815354640X^{6}Z^{11}+1481220854100X^{4}Y^{2}Z^{11}+33829983309X^{2}Y^{4}Z^{11}-25015764Y^{6}Z^{11}-18584054469648X^{4}YZ^{12}-292292176608X^{2}Y^{3}Z^{12}-129713584Y^{5}Z^{12}+24487659885456X^{4}Z^{13}+359151999684X^{2}Y^{2}Z^{13}+494669305Y^{4}Z^{13}+1023113532528X^{2}YZ^{14}+989595300Y^{3}Z^{14}-2072700316368X^{2}Z^{15}+3242776068Y^{2}Z^{15}-42358935744YZ^{16}+69564732336Z^{17} $ |
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.
