Canonical model in $\mathbb{P}^{ 12 }$ defined by 55 equations
| $ 0 $ | $=$ | $ x u + x v + 2 x r - x s + x a - y v + y s - y a + z u - z s - w u - t a - u b - v b + v d - r b + \cdots + a d $ |
| $=$ | $x u - 2 x v - 2 x r - x s + x a - 2 y u - y r - y s + y a - 2 z u - z v + 3 z s - 3 z a - w u + r b + \cdots - a d$ |
| $=$ | $2 x u - x v - x s + x a - y u - y v - y r - y s + y a + z u - z v + 2 z s - 2 z a + 3 w u + t a + \cdots - 2 a d$ |
| $=$ | $x v + 2 x r + 2 x a - 2 y u - y v - y r - y a - 4 z u + z v - 3 w u + v d + r b - r c - r d + a b - a c$ |
| $=$ | $\cdots$ |
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This modular curve has no real points, and therefore no rational points.
Maps to other modular curves
Map
of degree 2 from the canonical model of this modular curve to the canonical model of the modular curve
14.126.5.a.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle -u$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle s$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle -u-v-r+s-a$ |
| $\displaystyle W$ |
$=$ |
$\displaystyle -v-r$ |
| $\displaystyle T$ |
$=$ |
$\displaystyle -v$ |
Equation of the image curve:
| $0$ |
$=$ |
$ X^{2}+YZ+Z^{2}-4XW-2YW+2ZW+YT-ZT-WT $ |
|
$=$ |
$ X^{2}-XY-XZ+YZ+Z^{2}-XW-3ZW+W^{2}+2XT+YT-ZT+2WT $ |
|
$=$ |
$ 7X^{2}+4XY+2Y^{2}-3XZ-3YZ+2Z^{2}+2XW+YW+ZW-XT-YT-ZT-2WT+T^{2} $ |
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.
