LMFDB - Modular curve 280.504.13-14.b.1.1

Invariants

Level:	$280$	$\SL_2$-level:	$28$	Newform level:	$196$
Index:	$504$	$\PSL_2$-index:	$252$
Genus:	$13 = 1 + \frac{ 252 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 18 }{2}$
Cusps:	$18$ (none of which are rational)	Cusp widths	$14^{18}$	Cusp orbits	$3^{6}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$6 \le \gamma \le 24$
$\overline{\Q}$-gonality:	$6 \le \gamma \le 13$
Rational cusps:	$0$
Rational CM points:	none

Level structure

$\GL_2(\Z/280\Z)$-generators:	$\begin{bmatrix}27&196\\80&211\end{bmatrix}$, $\begin{bmatrix}87&132\\42&235\end{bmatrix}$, $\begin{bmatrix}167&124\\168&113\end{bmatrix}$, $\begin{bmatrix}193&82\\220&199\end{bmatrix}$, $\begin{bmatrix}197&192\\216&279\end{bmatrix}$, $\begin{bmatrix}207&40\\248&31\end{bmatrix}$, $\begin{bmatrix}207&84\\224&25\end{bmatrix}$
Contains $-I$:	no $\quad$ (see 14.252.13.b.1 for the level structure with $-I$)
Cyclic 280-isogeny field degree:	$96$
Cyclic 280-torsion field degree:	$9216$
Full 280-torsion field degree:	$2949120$

Models

Canonical model in $\mathbb{P}^{ 12 }$ defined by 55 equations

$ 0 $	$=$	$ 2 x y - 4 x w + 2 x u - x v + x r + 2 x s + x a - 2 x b - x c + 3 x d - 2 y^{2} - y z + 2 y w + \cdots + c^{2} $
	$=$	$x^{2} - 2 x z - x v - x r + x s + 2 x a - x c + x d - y w - y t + y u + 2 y v + y r + 3 y a - y b + \cdots + c^{2}$
	$=$	$2 x^{2} + 4 x y + 2 x z + x w - x t - x u + x r + 2 x a - x b + 2 x c + x d - 2 y^{2} + 2 y z + \cdots - c^{2}$
	$=$	$2 x^{2} + x y + 2 x z - 2 x t - x u + x v + x r - 2 x s - 2 x a + x b + x c - 4 x d - y^{2} + y w + \cdots - d^{2}$
	$=$	$\cdots$

[2*x*y - 4*x*w + 2*x*u - x*v + x*r + 2*x*s + x*a - 2*x*b - x*c + 3*x*d - 2*y^2 - y*z + 2*y*w + y*t + y*u + y*r - y*s - y*b + y*c + z*w + z*u + z*s - 2*w^2 - w*a + w*b + r*d - s^2 + 2*s*b - s*d + a*b + a*c - a*d + c^2, x^2 - 2*x*z - x*v - x*r + x*s + 2*x*a - x*c + x*d - y*w - y*t + y*u + 2*y*v + y*r + 3*y*a - y*b - y*c + y*d - z^2 - 4*z*w - 2*z*t + z*v - z*r - z*s + 2*z*a - w^2 - w*a + 3*w*b - r*a + r*b - r*c - s^2 - s*b + a^2 + a*d - b*c + c^2, 2*x^2 + 4*x*y + 2*x*z + x*w - x*t - x*u + x*r + 2*x*a - x*b + 2*x*c + x*d - 2*y^2 + 2*y*z + 3*y*w + y*t + y*u - y*v + 2*y*r - y*s - y*a - y*b + y*c + y*d + z^2 + z*w - z*t - z*r + z*s + w^2 + w*a - 2*w*b + r*a - r*b + r*c + r*d + 2*s*b - s*c + s*d + 2*a*b - a*c - 2*b^2 + b*c + b*d - c^2, 2*x^2 + x*y + 2*x*z - 2*x*t - x*u + x*v + x*r - 2*x*s - 2*x*a + x*b + x*c - 4*x*d - y^2 + y*w + 2*y*u - y*v + 3*y*r + y*s - y*a + 3*y*d + z^2 - z*t - z*u - 3*z*v + z*r + 3*z*s - z*a + w*a - w*b + r*a - r*b + r*c + s^2 + s*a - s*b + s*c + 2*s*d - a^2 + 2*a*b + a*c - a*d - b^2 - b*c + b*d + 2*c*d - d^2, 2*x^2 + x*y + 2*x*w - x*t + x*u + x*v + x*s + x*a - x*b - x*c - 3*y^2 - 3*y*z + 2*y*w - y*t + 3*y*u + 2*y*v + 3*y*r - 3*y*s - y*a - 2*y*c + y*d - z^2 - z*t + z*u + z*r - z*a + w^2 - r*a + r*b - r*c + r*d - s^2 - 2*s*b + s*c - s*d - b*c + 2*b*d, x^2 - 2*x*w + 2*x*t + 2*x*u - x*v + x*r - x*a - x*b - 2*x*c + x*d + y^2 + 3*y*z - y*w - y*t - y*u - y*v + 2*y*r - y*s - y*a - y*b + 2*y*c + y*d + z^2 + 2*z*w - z*u - 2*z*v + z*r + z*s - z*a - w^2 - w*b - r*a + r*b - r*c + s*a + s*b + 2*s*c - s*d - a^2 + 2*a*b + 2*a*c - 2*a*d - b^2 + b*c + b*d + c^2, x^2 + 2*x*y - 2*x*t - x*u + x*r + x*s - x*b - x*c - 2*y^2 + 3*y*w + y*t + y*u + 2*y*v - y*s + 2*y*c - y*d + z^2 - 5*z*w - z*t - z*r - 2*z*a + w^2 + r*a - r*b + r*c + r*d + s*a - 3*s*b + 2*s*d - a*b - 2*a*c + a*d + b^2 - b*c - c*d, x^2 + x*y + 3*x*w - 2*x*u - 2*x*r + 2*x*a - x*c + x*d - y*w - 2*y*t + 2*y*u + y*v - y*s + 3*y*a - 4*y*c + 2*y*d - z^2 + 2*z*w - 2*z*u + z*v - z*r - 2*z*s + 2*z*a + w^2 + w*a - r*c - r*d - s^2 - s*a - s*c - s*d + a^2 - a*b - a*c + 2*a*d + 2*b*c - c^2 - c*d + d^2, x*y + 2*x*z - x*w - x*t - x*u + x*v - 2*x*s - x*b + 3*x*c - x*d + 3*y*w - y*r - 2*y*a + y*b + 2*y*c - z^2 + 2*z*w + z*u + z*v - z*r - z*s - w*b + r*a - 2*r*b + 3*r*c - r*d + s^2 - s*a + 2*s*b - s*c + s*d - a*c + a*d - b*c - b*d, x^2 + x*z + 2*x*t - x*v + 2*x*s + 2*x*a - x*b + 3*x*c + x*d - 3*y^2 + 3*y*w + y*t + 4*y*r - 2*y*s - 4*y*a - y*b + y*c - y*d + 3*z^2 + 2*z*w + 2*z*t - z*u + 4*z*r - z*s - z*a - w*a - w*b + r*c + 2*r*d + s*a + s*d + a*b - a*c - b^2 - b*c + b*d, x^2 - 3*x*y + x*z - 2*x*w - x*t + 2*x*u + 2*x*v + x*r - x*s - 2*x*b - x*d + 2*y^2 - 2*y*z - y*w - y*t - y*v - y*r + 2*y*s + 2*y*b - y*c + y*d - 2*z^2 + 3*z*w - 3*z*v + 5*z*s + 3*z*a - 2*w^2 - w*a + w*b + r*a - r*b + r*c - r*d + s^2 - s*b + s*c - a*b + a*c + a*d + b^2 - b*c - b*d + c^2 + c*d, 2*x*y - 2*x*w + x*t - x*u - x*v + 2*x*r - 2*x*s + 2*x*c - y^2 + y*z + 3*y*w - y*t + 2*y*u - y*r - y*a - y*c + y*d + z^2 + z*w - z*r - z*s - 3*z*a - w^2 + 2*w*a - w*b + 2*r*a - r*b + r*c - s*a + 4*s*b - s*c - s*d + 2*a*b + a*c - a*d - b^2 + 2*b*c - c^2 + c*d, x^2 + x*y + x*t - x*s - x*a - x*b + 2*x*c - 3*x*d + y*z - y*w + y*u + y*r + y*s + y*a - y*b + y*c + 3*y*d - 2*z*w - z*v - z*a + 2*w*a - w*b - 2*r*a - 2*r*d + s*a + 2*s*b + s*c + 2*a*b + 3*a*c - 2*a*d - b^2 + b*d + 2*c*d - d^2, x*y + x*w + x*t - x*v + 2*x*r - x*a + x*b - x*c + 2*x*d - y^2 + y*w - y*t + y*u - y*v - 2*y*s - 2*y*a + y*b - y*c - y*d + 2*z*w - 2*z*t + 2*z*u + 2*z*v - z*r - 2*z*a + 2*w^2 + w*a - 2*w*b - r*s + r*b - 2*r*c + 2*r*d + s*b - s*d - a^2 + a*b + a*c - 2*a*d - b^2 + b*c + b*d - c^2, x^2 + 3*x*y + 4*x*w - 4*x*t + 2*x*v + x*s + 2*x*a - x*b - 2*x*c + 2*x*d - y^2 + y*t + y*v - 2*y*s + y*a - y*c - y*d - 2*z^2 - z*w - 2*z*t + z*u + z*v - 3*z*r + z*a + 2*w^2 + 2*r*s + 2*r*a - r*b + r*d - s^2 - s*a - 3*s*b - s*c - 2*a*b - 3*a*c + 2*a*d + b^2 + b*c - c^2 - 2*c*d + d^2, x*y + x*w + 2*x*a + 2*x*c + x*d + y*w - y*t - y*r - y*s - y*a + y*b - y*c - y*d - z^2 - 2*z*w - z*t + 2*z*u + z*v - z*r + w^2 + v*c - r*s - r*a + r*b - s*a + 2*s*b - 2*s*c + a^2 - a*c + a*d - b^2 - c^2, x^2 + 3*x*y + x*z + x*w - x*t - x*v - x*r + x*s + 2*x*a - x*b - x*c + 3*x*d - y^2 + 2*y*z + y*v + 2*y*r - 2*y*s - 2*y*b + y*d + z*w + 2*z*v + z*r - 5*z*s + w^2 - w*a + r^2 - 2*r*a - s^2 + s*b - s*c + a*b - 2*a*c - b^2 + b*c + b*d - 2*c*d, 2*x^2 + 2*x*y + x*z + 3*x*w + x*u + x*v + x*s + 3*x*a - 3*x*b + 2*x*d + 2*y*w - y*u + y*v - 3*y*s - y*a + y*b + 3*y*c - y*d - 2*z^2 - z*w + z*u - z*v - z*r + 2*w^2 + w*a - 2*w*b - v*d - 2*r*a - s^2 - s*a + s*b + s*c - 2*s*d + a^2 - a*c + a*d - b^2 + 2*b*d - 2*c*d + d^2, 2*x^2 + x*w - x*t - x*u + x*v - 2*x*r + 3*x*a - x*b + 4*x*c - x*d + y*z + y*u + 2*y*r + y*s + y*a - y*b - 2*y*c + 3*y*d - 2*z*u - z*v + z*s + 3*z*a - w^2 - w*a + 2*w*b - v*c - r*b + 2*r*c - r*d - s*b + s*d + a^2 + 2*a*d - 3*b*c + c^2 + c*d, x^2 + 2*x*z - 2*x*w - 2*x*t - x*u + x*v + x*r - x*s - x*a - x*b - 2*x*d + y^2 + y*z + y*u - y*v - y*r + 2*y*s + y*a + y*b + 2*y*d - z*w - 2*z*t - 2*z*r + 3*z*s + 2*z*a - 2*v*c + v*d + r*a - 2*r*b + 2*r*c - r*d + s^2 + s*a - s*b + 3*s*d - a*c + a*d - b*d + c*d - d^2, 2*x^2 - x*t + x*u + x*v - x*r + 2*x*a - 2*x*b - x*c - 2*y*z - y*t + 2*y*u + y*r + y*a + y*b - 2*y*c + 3*y*d - 2*z^2 + z*w - z*u - 2*z*v + 2*z*s + z*a - w^2 + w*b - v*b - r*s - r*a - 2*r*d - s^2 - s*a + s*b - s*d + a^2 - a*b + a*c + a*d + b^2 - b*c + c^2, x^2 + x*y - 2*x*w + 2*x*t - 2*x*v + 2*x*r - x*s + x*a + x*c + 2*x*d + 3*y*z + y*w - y*t + y*r - y*b + y*c + z^2 - 2*z*t + z*u + 2*z*v - z*r - z*s + z*a - w^2 - v*a - r*c + 2*r*d + 4*s*b - s*d + 4*a*b + a*c - a*d - 3*b^2 + b*c + b*d + c*d, x^2 - x*y - x*z + x*w - x*t + 2*x*u + 2*x*r + x*s + x*a - x*b - 2*y*z - 2*y*w + y*t + 2*y*s + y*a - 2*z^2 - 2*z*w - 2*z*t + 3*z*u - z*r + 3*z*s + 2*z*a + w*b + v*r - r*c + s*a - s*b + s*d + a*c - a*d + c*d - d^2, 2*x^2 - x*y + 2*x*w - x*u - x*r - x*b - x*c - x*d - y^2 - y*z - y*t + 2*y*u + y*v + 2*y*r - y*s + y*b - 2*y*c + 2*y*d + z*w - 2*z*u + z*r - z*s + w^2 + u*c - r*s - r*a - r*b - r*d + s*a - 2*s*b + s*c + s*d - a*b + a*d + b^2 - b*c, x^2 - x*z - x*w - 2*x*t - x*s + x*a + x*b + 2*x*c - x*d + y*z + y*t + y*u + 3*y*s + 2*y*a - 2*y*b + 2*y*d + z^2 - 3*z*w - z*t - z*v - z*r + 3*z*s + 2*z*a - w^2 - w*a + 2*w*b - u*c + v*a + v*b - r*s + r*a + r*c + s^2 - s*b - s*c + 2*s*d + a*b - b^2 - 2*b*c + c^2 + c*d - d^2, 2*x^2 + x*y + x*z + 2*x*w - x*u - x*r + x*s - 2*x*b - x*d + 2*y*z - y*t + y*v + 2*y*r - y*s + 2*y*c + y*d - 2*z*w - z*t - z*u - z*s + 2*w^2 - w*b + u*b - v*a - v*b + v*c - 2*r*a - r*d + 2*s*a - s*b + 2*s*d - a*c + a*d - b*c + b*d - c*d, x^2 - x*y - x*z - 2*x*w + 3*x*u + 2*x*r - x*s + x*a - 2*x*b + x*d + y^2 + y*z - y*w - y*u + y*s - y*b + y*c - 2*z^2 - 2*z*t + 2*z*u - 2*z*r + 2*z*s + 2*z*a - 2*w^2 - w*a + 2*w*b + u*b - v*a + v*b - v*c + r*s + 2*s*b + s*c - s*d + 2*a*b + a*c - b^2 + c^2 + c*d, 3*x*w + x*t + x*v + x*r + x*a - x*b + 3*x*c + y^2 + 4*y*z - 2*y*w + y*t - 3*y*u - y*v - y*r - y*a - y*b + y*c - 2*y*d + 2*z^2 - 2*z*w + z*t + 2*w^2 + w*a - 2*w*b + v*r + v*a + v*c + v*d + s^2 + s*a - s*c + s*d - a*c - b^2 + 2*b*c - 2*c^2, 2*x^2 - x*z - 2*x*w + x*t + 3*x*u + x*r - x*s + 2*x*a - 2*x*b - 2*x*c + x*d + y^2 - 2*y*t + y*u + 2*y*v + 2*y*a - y*b + 2*y*d - 2*z^2 - z*t + z*u - z*v - z*r + z*s + z*a - 2*w^2 + w*b + u*a - u*b - r*a + r*b - r*c - r*d - s^2 - s*a + 2*s*b + s*c - 3*s*d + a^2 + a*b + a*c - b^2 + b*c + b*d + c^2, x*y + x*z - 3*x*w + x*u - x*v + 2*x*s - x*a - 2*x*b + x*d - y^2 + 2*y*z + y*t - y*u - y*v + 2*y*r - 2*y*a - y*b + 2*y*c + 2*z^2 + 3*z*w + 2*z*t - z*u - z*v + 2*z*r + z*s - z*a - w^2 - w*a - w*b - u*s - v*a - r*b + r*c + 2*s*a + s*c + s*d - a^2 + a*c - a*d + b^2 - b*c - b*d + c^2, 2*x^2 - 2*x*y + x*z - x*w + x*t + 2*x*u + 2*x*r + x*a - 2*x*b - 2*x*c + 2*x*d + y^2 - y*z + y*w - 2*y*t - y*s - 2*y*a + 2*y*b - z^2 + 2*z*w - z*t - z*v + z*r + z*s - w*a + u*r - v*b + r^2 - r*s - r*a - r*c + r*d + s*c - s*d - b*c + b*d + c^2 - c*d, x^2 - x*y - x*z + 2*x*t - x*r - 2*x*s - x*a - 2*x*d - 2*y*t + 2*y*u + y*v + y*r + y*a - y*b - 2*y*c + 3*y*d + 2*z*w + z*t - 2*z*u - z*v + z*r - z*s - z*a - w^2 + w*a + t*c - r*s - 2*r*a + r*b - r*c - 2*r*d + s*b + 2*s*c - 2*s*d + a*b + 3*a*c - a*d - b*c + b*d + c^2 + c*d, x^2 + x*y - x*z + 3*x*w - x*t - x*u - x*r - 2*x*s + 2*x*b + x*c - 2*x*d + y*w - 2*y*t + y*u + 2*y*v + y*r - y*s - y*a + y*d - 2*z^2 - 2*z*w - 2*z*t + z*u - z*r - 2*z*s - 2*z*a + w^2 + w*a + t*b + v*c - v*d - r*a + r*b - r*d - s*a + a*b - b^2 - b*c + b*d, x^2 + 3*x*y - x*w + x*r - 2*x*b - y^2 + 2*y*z + 2*y*w - y*t + 2*y*u + 2*y*v - 2*y*s - y*b + 2*y*d + z^2 - z*w - z*u - z*v - z*r - z*s - 3*z*a + 2*w*a - w*b - u*v + v*a - v*c - r*b + r*c - r*d - s^2 + s*b + s*c - s*d + a*b + a*c - a*d + b*c + b*d, 3*x*w - x*t + x*v - x*r - x*s - x*a + x*b - x*c - y*s - y*a - z^2 + 3*z*w - z*t + z*u + 2*z*v - z*r - z*s + 2*w^2 - w*b + t*a - r*s - r*a - r*c - s*a - s*d - a^2 - a*d - b*c + b*d - c*d, x^2 - x*y - x*z + 3*x*w + 3*x*t - 2*x*u - x*v - x*r + x*a - x*c - y*w - 2*y*t + 2*y*u + 2*y*v - y*s + 2*y*a - 2*y*c + y*d - 2*z*w - z*u + 2*z*v - 4*z*s + 2*w^2 + 2*w*a - w*b + t*d + v*a - v*c - 2*r*a + r*b - 2*r*c - s^2 + s*c - s*d + a^2 - b^2 + 2*b*c + b*d - c^2, x*z + 2*x*w + x*t - 3*x*u - x*v + x*s + 2*x*a + 4*x*c + 2*y*t - y*u - y*v - y*r + 2*y*s + y*a + y*c - y*d + z^2 - z*w + z*t - z*u + z*v + 2*z*a + w^2 + w*a - w*b + t*s + v*r - v*b - r*s + r*a - r*b + r*c + s^2 + s*a - s*c + 2*s*d + a^2 - a*b - a*c + a*d - b*d - c^2, 2*x^2 - x*y + x*z + 2*x*w - 2*x*t + 3*x*v + 2*x*r - 2*x*s - 2*x*b + 2*x*c - 3*x*d - y^2 - 2*y*z + 2*y*w + y*u + 2*y*v - y*r - 2*y*a + y*b - 2*z*w + z*t - 2*z*v + z*r + z*s - 2*z*a + w^2 + w*a - w*b + t*r - u*c + r^2 + r*a - 2*r*b + 2*r*c + s^2 - 3*s*b + s*c - a*b - a*c + a*d + b^2 - 2*b*c + b*d, x*w - x*u + x*v - x*r - x*s - x*a - x*c - x*d + y*w - y*t + y*u + y*v - y*r - y*s + y*d + z*w + z*t - z*u + z*v - 3*z*s - 2*z*a + w^2 + w*a - w*b - u*v + v*r - v*s - 2*r*s - r*a - 2*r*d - a*b + b^2 - c*d, x*y - x*w - 2*x*t + x*u + 2*x*v + x*r - x*s - 2*x*a - 2*x*b - x*c - x*d - 2*y^2 - 2*y*z + 2*y*w + y*t + 2*y*u - y*r - y*s - y*a + y*d - z^2 + 2*z*w + z*t + z*u - z*r - 3*z*a + w*a - w*b + t*v + v*r + r*a - r*b + r*c - r*d - s*b + s*c - s*d - a^2 - a*b + a*c - a*d + 2*b^2, x^2 + x*z + 2*x*w - 3*x*u - x*a + x*c - 2*x*d - 2*y^2 - y*z + 2*y*w + 2*y*u + y*v + y*b - y*c + y*d + 3*z^2 + 2*z*t - 3*z*u - z*v + 2*z*r - z*s - 2*z*a + 2*w^2 + 2*w*a - 2*w*b + t*u + v*a - r*s - 2*r*b + s*a - s*b + s*d + b*d - c^2, x*y + 3*x*t + x*u - x*v + x*s + x*a - x*b + 2*x*c + x*d - y^2 + y*w + 2*y*r - 2*y*s - y*a - y*b + y*c + 2*z*w + z*u + z*v + z*r - z*s - w*b - t^2 + v*c - r*a + r*b + 2*s*b - s*d + a*b + a*c - a*d - b^2 + b*d, x^2 + 2*x*y + x*w - x*t + x*v + 2*x*s + 2*x*a - 2*x*b + x*d - y^2 - y*z + 2*y*w + y*t + y*u + y*v - y*r - y*s + 2*y*a + y*c - z^2 - 4*z*w - z*t + z*u - 2*z*r + z*s + z*a + w^2 + w*s + v*a - r*a - s^2 - s*b + a^2 - a*b - a*c + a*d - b*c + b*d - c*d, x*y + x*w - x*t - 2*x*u - x*r + x*s + 2*x*a + 2*x*d + y^2 + y*z + y*t - y*u - y*v - 2*y*r + y*s + 3*y*a + y*c - y*d - z^2 - z*w - z*t - z*u + z*v - 3*z*r + z*s + 3*z*a - w*v + w*b - r*s + r*a - s*b - s*c + s*d + a^2 - 2*a*b - a*c + 2*a*d + b^2 - 2*b*d - c*d + d^2, 3*x*y + x*z - x*w - x*t - x*u - 2*x*r + x*s + x*a - x*c - 2*y^2 + y*w + y*t + y*u + 2*y*r - y*s + 2*y*a - 2*y*b + y*d - z*w - z*u + z*v - z*s + z*a - w^2 - w*t + w*b + v*d - r*a + r*b - r*d - s^2 + s*b - s*c + s*d + a^2 - a*c + a*d + b*c - b*d, x*y - x*w + 2*x*u + x*c - y^2 + y*z - y*w + 2*y*t - 2*y*v + 2*y*r + y*s - y*a - 2*y*b - y*c + 2*y*d + 2*z^2 + 3*z*w + 2*z*t - z*v + 2*z*r + z*s - z*a - z*c - w^2 - w*b - u*b + 2*s*b - s*d - a^2 + 2*a*b + 2*a*c - 3*a*d - b^2 + b*c + b*d + c*d - d^2, x*z + x*w - x*t - x*u + x*r - x*a - x*b - x*c + y^2 + y*z + y*t - y*u - y*v - 3*y*r + y*s + 2*y*b + y*c - y*d + z^2 + z*t - z*u - z*v - z*r + 2*z*s - z*a + 2*w^2 + 2*w*a - 3*w*b + w*d - r*s + r*a - 2*r*b + r*c - r*d + s^2 + s*a - s*b - s*c + 2*s*d - 2*a*b - a*c + a*d + b^2 + b*c - b*d - c^2 - c*d, x^2 + 3*x*y + 2*x*z - 2*x*w - x*t + x*u - x*v - 2*x*s - x*a + 2*x*b - x*d - y^2 + y*w + 4*y*r - y*s - y*a - 2*y*b + 2*y*c + 2*y*d - z^2 + 2*z*w - z*t + z*u - z*v + z*r - w^2 - w*a - u*d - v*a + v*b + v*c - v*d - r*a + r*b - s*a + 3*s*b - s*d - a^2 + 4*a*b + a*c - 2*a*d - 3*b^2 - b*c + 2*b*d + c^2 + c*d - d^2, x*z - 3*x*w + 2*x*t - x*u - 2*x*v + x*r - x*a + x*b + x*d - y^2 + y*w + y*u - 2*y*v + 2*y*r - y*a - y*c + y*d + 2*z^2 + 5*z*w + z*t - 2*z*u - z*v + 2*z*r + z*s - 2*w^2 - w*a - w*c - u*b - v*c + 2*r*a - r*b + r*d + s*b - a^2 + a*b + a*c - a*d + b*c - b*d + c*d, x*z - x*w - 2*x*t + 2*x*u + 2*x*v + 2*x*a - x*b + 2*x*c - 2*y*z + y*w - y*v - 2*y*a + y*b - 2*y*c - 2*z^2 + 2*z*w + 2*z*u - z*v + 3*z*s + z*a - w^2 - w*r + w*b - v*a - v*c + r*c - s*a + s*b - s*d + a^2 + a*d - b*c + c*d, x^2 + 2*x*y + x*w - 2*x*t + x*a - x*b - 2*x*c + 2*x*d + y^2 + 3*y*z - y*u - y*r + y*a + 2*y*c - z*w - z*u - z*v - 2*z*r + w^2 + w*u + w*s + w*a - w*b - v*a + v*c - v*d + r*a - r*b - a*c + a*d + b*c - 2*c*d + d^2, 3*x^2 - x*y + x*z + x*r - 3*x*s + x*a + 2*x*c - 2*x*d + 2*y^2 + 2*y*z - y*w - 2*y*t - y*v + y*r + 3*y*s + 2*y*d - z^2 - 2*z*t - z*v - z*r + 3*z*s + 2*z*a - z*d - w^2 - v*a + v*c - r*s + r*b - r*d + 2*s^2 + s*a + s*b + 2*s*d + 2*a*b + a*c - 2*b^2 + 2*c*d - d^2, 2*x^2 + x*y - x*t - x*u - x*v - x*s + x*a + x*b + x*c - x*d - y^2 + 2*y*w - y*t + y*u + 3*y*v + 3*y*r - y*b + y*c + y*d - 3*z*w - z*t + z*r - 2*z*s - z*b - w^2 - w*a + 2*w*b - v*a + v*c - v*d + r*s + r*a - r*b + r*c + r*d - s*b + s*d + 2*a*b - a*c + a*d - b^2 - 2*b*c + b*d + c^2, x^2 + x*y + x*w - x*u - x*v + x*s - x*b - 2*x*c + 2*x*d + y^2 + 3*y*z - y*w - y*u - y*v - y*r - y*s + 2*y*a + 2*y*c - z*u - 2*z*r + z*a + w^2 + w*a - w*b + v^2 + v*c - v*d - r*s - r*a - 2*r*c - s^2 + s*a + a*c + b*c - c*d + d^2, x^2 + x*y + 2*x*w + x*t + x*r + x*a - x*b - x*c + 2*x*d - y^2 + y*w - y*t + y*v - y*r - 2*y*s + y*a - y*c - y*d + z*w - z*u + z*v - z*r - z*s + w^2 + w*a - 2*w*b + u^2 + u*v - u*c + v*b + v*c - r*s + r*b - 2*r*c + r*d - 2*s*d - b^2 + 2*b*c + b*d - c^2 - c*d + d^2]

Rational points

This modular curve has no $\Q_p$ points for $p=5,17$, and therefore no rational points.

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 14.84.5.b.1 :

$\displaystyle X$	$=$	$\displaystyle d$
$\displaystyle Y$	$=$	$\displaystyle x-y+r-s$
$\displaystyle Z$	$=$	$\displaystyle z-w-u-s-a$
$\displaystyle W$	$=$	$\displaystyle -u-a-d$
$\displaystyle T$	$=$	$\displaystyle x+w+v+a-b+c$

Equation of the image curve:

$0$	$=$	$ Y^{2}+XZ-YZ-XW-YW+ZW-W^{2}+T^{2} $
	$=$	$ X^{2}+2XY-Y^{2}-2XZ-YZ+Z^{2}-T^{2} $
	$=$	$ 2X^{2}+2XY-Y^{2}+XZ-2YZ-Z^{2}+2T^{2} $

Modular covers

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve	Level	Index	Degree	Genus	Rank
7.42.1.b.1	$7$	$12$	$6$	$1$	$0$
40.12.0-2.a.1.1	$40$	$42$	$42$	$0$	$0$

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
280.252.7-14.a.1.1	$280$	$2$	$2$	$7$	$?$
280.252.7-14.a.1.4	$280$	$2$	$2$	$7$	$?$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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Abelian varieties over $\F_{q}$
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