LMFDB - Modular curve 60.480.13-60.nl.1.4

Invariants

Level:	$60$	$\SL_2$-level:	$60$	Newform level:	$3600$
Index:	$480$	$\PSL_2$-index:	$240$
Genus:	$13 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$
Cusps:	$16$ (none of which are rational)	Cusp widths	$5^{4}\cdot10^{4}\cdot15^{4}\cdot30^{4}$	Cusp orbits	$4^{4}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	$0$
$\Q$-gonality:	$4 \le \gamma \le 6$
$\overline{\Q}$-gonality:	$4 \le \gamma \le 6$
Rational cusps:	$0$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:	30N13
Rouse, Sutherland, and Zureick-Brown (RSZB) label:	60.480.13.1160

Level structure

$\GL_2(\Z/60\Z)$-generators:	$\begin{bmatrix}4&49\\9&16\end{bmatrix}$, $\begin{bmatrix}7&38\\18&43\end{bmatrix}$, $\begin{bmatrix}25&54\\36&5\end{bmatrix}$, $\begin{bmatrix}25&56\\24&55\end{bmatrix}$, $\begin{bmatrix}56&11\\51&28\end{bmatrix}$
Contains $-I$:	no $\quad$ (see 60.240.13.nl.1 for the level structure with $-I$)
Cyclic 60-isogeny field degree:	$12$
Cyclic 60-torsion field degree:	$192$
Full 60-torsion field degree:	$4608$

Jacobian

Conductor:	$2^{27}\cdot3^{17}\cdot5^{26}$
Simple:	no
Squarefree:	no
Decomposition:	$1^{13}$
Newforms:	50.2.a.b$^{2}$, 75.2.a.a$^{2}$, 75.2.a.b$^{2}$, 150.2.a.b, 3600.2.a.bg, 3600.2.a.bk$^{2}$, 3600.2.a.l$^{2}$, 3600.2.a.o

Models

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

$ 0 $	$=$	$ y r - y a + y b - y c - y d + z r + z s + u r + u s $
	$=$	$x r + x s + y r - y s + y c - 2 y d + u r + u s - v r - v s$
	$=$	$x r + x a + x b + x c + x d - 2 y b - z r - u r$
	$=$	$3 x r - 2 x s - 2 x a - x c + x d + y r + y a - y c - z r + z s + u s + v a + v b + v c + v d$
	$=$	$\cdots$

[y*r - y*a + y*b - y*c - y*d + z*r + z*s + u*r + u*s, x*r + x*s + y*r - y*s + y*c - 2*y*d + u*r + u*s - v*r - v*s, x*r + x*a + x*b + x*c + x*d - 2*y*b - z*r - u*r, 3*x*r - 2*x*s - 2*x*a - x*c + x*d + y*r + y*a - y*c - z*r + z*s + u*s + v*a + v*b + v*c + v*d, x*r + 2*x*s + x*a + x*c + x*d - y*r - 2*y*s - y*d + z*r - z*b + u*s - 2*u*a - u*c + u*d + v*s - v*a - v*b, 3*x*r - x*s - 2*x*a - x*b - x*c + x*d - 2*y*r - y*a - y*b + y*c + 2*z*r - u*r - u*s - v*r - v*s + v*b, 2*x*r + x*s + x*a + x*b - x*c + y*r + 2*y*a + y*b + z*s + t*b + u*r + 2*u*s - 2*u*a - u*b - u*d + v*r - v*a + v*b, x*r - 2*x*s + 2*x*b - 3*x*c + x*d - y*a - 2*y*b + y*c + y*d + z*r + z*s - z*b - u*r - 2*u*a - u*c + u*d - v*r - 2*v*a + v*d, x*r - x*b + x*c + x*d - y*r + y*a + y*b - y*c + 2*z*r + z*s + 2*z*a + 2*z*b + t*a + t*b - u*r + u*a - u*d - v*s + v*b + v*c, x*s + 2*x*a + x*b + x*d + 2*y*a - y*d + z*r - z*s - u*r + 2*u*s + v*s - 2*v*a - v*b, x*r + x*b - 2*x*c + y*r + y*a - y*c - y*d - 2*z*r - z*a - z*b - t*b - t*d + 2*u*s + u*c + v*r + v*s + v*a, x*r + x*s - 2*y*r + y*d + z*r - z*b - t*a - t*b + t*c - u*a - u*b + u*c + v*r + v*s - v*c - v*d, 2*x*r - x*s - 2*x*a - 2*x*b + x*c + 2*x*d - y*r - y*s + y*a - y*d + z*r - z*s - t*s - u*r - v*r + v*c, x*r - y*r + y*s + y*c - y*d + z*r - z*s + z*b + t*r + t*s + u*r + 2*u*a + u*c - u*d - v*s + v*b - v*c - v*d, x*r - x*a + x*b + y*r + 2*y*a + y*d - z*r + z*s + w*c + t*a + t*b + u*s - u*a - u*c + v*c + v*d, x*a - x*c - x*d + y*s + y*a + y*d - z*s - z*a - z*b + w*a + t*s - t*a - t*c - u*r - u*a + v*r + v*s - v*a, x*r + x*b + y*r + 2*y*a - 2*z*r + z*s + z*a + w*s + w*a + w*c + u*s + v*a + v*c + v*d, x*r - x*a + x*c - y*b + z*r + w*r + t*s, x*r + x*s - x*a - x*b + x*c - 2*y*r - y*s - y*a + y*b - y*d + z*r + w*r - t*s + u*r + v*a - v*c - v*d, 2*x*s + x*a - x*c - x*d + y*b - z*a - z*b - z*d - t*a - t*c + u*s - u*a + v*r + v*s - v*a - v*c, x*a + x*b - x*c + y*s - y*a - y*b + z*r - z*a - z*b + z*c - t*r - u*r - v*a - v*c, x*s - x*b + x*c - y*r + y*s - y*a - y*d + 2*z*r - z*s - z*a + z*d - w*a - w*c - t*a - u*d - v*a - v*c - v*d, 2*x*r - x*a + x*c + y*s + y*a - 2*y*c - z*a + w*s + w*a - w*d + v*r + v*s + v*a + v*c, 3*x*r - x*s - x*a - x*b + x*c + x*d - y*r - y*a - y*c + y*d + z*s + z*a + z*b - w*a - w*b + t*r - t*a + t*d - u*s + u*a + v*a + v*b, x*y + x*u - 2*y^2 + y*z - y*w - y*u - y*v + z^2 - u*v, 2*x^2 + x*y - 2*x*z + x*w - x*t - 2*x*u - y*w - y*t + y*u - 2*z^2 + z*t - z*u + z*v - w*t - w*u - t^2 - t*u + u^2, 2*r*s - r*a - 2*r*b + r*c - 3*s*a - s*b + s*c - s*d - 2*a^2 + a*b - 3*a*c - a*d + b^2 - b*c - c^2 + d^2, r^2 + r*s + r*c + 3*r*d - 2*s^2 - s*b + 2*s*c + s*d + 2*a^2 + 2*a*b - 2*a*c - 4*a*d + b^2 - b*c - 2*b*d - c*d, 2*r^2 + r*s + 4*r*a + r*b + r*c + s^2 + 2*s*a - s*b + s*d + 2*a^2 + 2*a*b - 2*a*c + a*d + b^2 - 2*b*c + c^2 - d^2, x^2 - 3*x*z - x*w - x*t - 2*x*u - x*v + y*z + y*t - y*v + z^2 - 3*z*t + 2*z*u - w^2 - 2*w*t + w*u + t*v - u*v, x^2 - x*y - x*t - x*v - 3*y*z - y*w - y*u + y*v - z*w - 3*z*t + 2*z*u - w^2 - 2*w*t + w*u - w*v + t*v, 2*x*y + 2*x*z + x*w + x*u - y*z + 2*y*w + y*t + 3*y*v - z*w - z*t - z*u - z*v + w*t + 2*w*u + w*v + 2*u*v, x^2 + 3*x*y + x*z + x*w + x*v - 2*y*z + y*w - 2*y*t - y*u + 2*y*v - 2*z^2 + z*w - z*u + 2*z*v - w*t - t^2 - t*u - t*v + u^2 + u*v, 2*x*y + 2*x*z + x*w - 2*x*u + y*t + z^2 + 2*z*w - 2*z*t + z*u - w*t + w*u - u*v, x^2 - 4*x*y - 2*x*z - x*t - x*u - x*v + 3*y*z + 2*y*w - y*t - y*v + 2*z^2 - z*v + t*v + u*v, 2*x^2 - 2*x*z - x*w - 2*x*t + x*u + 2*x*v + y*z + 2*y*t - y*v - z^2 + 2*z*w + 3*z*v + w^2 + 2*w*v - 2*t*v - u*v, x^2 + 2*x*y - x*z + 2*x*w + 3*x*t + 4*x*v + y*t + z^2 - 3*z*t + 2*z*u + z*v + 2*w*u + w*v + t^2 + t*u + t*v - u^2 - u*v - v^2, 5*x^2 + x*y + x*z - 2*x*w + 4*x*t + x*u + x*v + 2*y^2 - y*z + y*w - y*t - y*u - y*v - 2*z*w + 3*z*t + z*u - 3*z*v + w^2 + w*t - 3*w*u + 3*w*v + t^2 + t*u + 4*t*v - u^2 - 3*u*v + 3*v^2 + r^2, 6*x^2 + 4*x*z - 4*x*w + 5*x*t - 3*x*u + 2*x*v - 2*y^2 + 2*y*z - y*w - y*t - y*u - 2*y*v - 2*z^2 - 2*z*w - 2*z*u + z*v - 2*w^2 + w*u + w*v - t^2 - t*u + 3*t*v + u^2 + 3*u*v + 3*v^2 - r*s, 4*x^2 - x*y - x*w + x*u - 8*x*v + 2*y*z + 2*y*w - 4*y*t + 2*y*u + 2*y*v - z^2 - z*t + z*u + z*v + w*t + w*u + 3*w*v + t^2 + t*u - 2*t*v - u^2 - 8*u*v - 4*v^2 + r*s + r*a + r*c, 2*x^2 - x*y - x*z - x*w + 3*x*t - 2*x*u + 2*x*v + 3*y^2 - 2*y*z - 3*y*w + 6*y*t - 8*y*u - 3*y*v + 4*z^2 + 2*z*w + 3*z*t - z*v + 2*w^2 + 3*w*t - 6*t*u + t*v - 3*u^2 + u*v + v^2 - r*s + r*b - r*c + s*a + a^2 + a*c, 3*x^2 + 2*x*y - 3*x*w + x*u + x*v - 2*y^2 - 2*y*z + 3*y*w + 4*y*t + 3*y*u - 8*y*v - z^2 + z*w - 3*z*t - 3*z*u - 2*z*v - 2*w^2 + w*t + 2*w*u + 2*t^2 - t*u - 2*t*v + 4*u^2 + 3*u*v - 4*v^2 - r^2 + r*a - r*d + s*b - 2*s*c + a*d + c*d, 3*x^2 - x*y - x*w + 5*x*t - 4*x*u - 2*x*v + y^2 - 3*y*z - 2*y*w - 3*y*t - y*u + 2*y*v + 5*z^2 + z*t - 2*z*u + 4*z*v + 4*w^2 + 2*w*t + 4*w*u + 3*w*v - 3*t^2 + 3*t*v - 3*u^2 - 4*u*v + 3*v^2 + r^2 - r*a + r*d - s*b + s*c - a*d - c*d, x^2 + 2*x*w + 5*x*u - 5*x*v + 2*y^2 + y*z + 2*y*w - 2*y*t + 2*y*u + y*v - 3*z^2 + 4*z*w + 2*z*t - 2*z*u + 2*z*v - 3*w^2 - w*u - 6*w*v - t^2 - t*u + u^2 - 2*u*v - 4*v^2 + r*s + r*a, 5*x^2 - 2*x*y + x*z - 4*x*w + x*t - 4*x*u + x*v - 2*y^2 - y*w + y*t - 3*y*u - 2*y*v - 2*z^2 + 2*z*w + 6*z*t + z*u - 4*z*v + 2*w*t + 2*w*u - w*v + 9*t^2 - 6*t*u - t*v + 6*u^2 + u*v + 3*v^2 - r*b - s*a - s*b + s*c - a*c + b^2 - b*c - c^2 + c*d + d^2, x^2 - x*y - 3*x*t + x*u + 4*x*v - 3*y^2 - y*z + 6*y*w + 2*y*t - y*u - 4*z^2 - 2*z*w + 3*z*t - z*u - 4*z*v + 2*w*t - 3*w*u - 4*w*v + 2*t^2 + 8*t*u - 2*t*v + u^2 - 5*u*v - 2*v^2 - r^2 - r*s - 2*r*a - r*c - r*d + s*b - s*c - a^2 - 2*a*b + 2*a*c + a*d - b^2 + 2*b*c + b*d - c^2, 3*x^2 + 2*x*y + x*z + x*w - 4*x*t + x*u - x*v - 2*y*z + 5*y*w - 2*y*t + y*u - 4*y*v - z*w + 9*z*u - z*v - w*t - 2*w*u - w*v + t^2 + 4*t*u - 3*t*v - 7*u^2 + 2*u*v - 5*v^2 - r^2 + r*c - s^2 - s*a + s*b - s*c + a*b - a*c, x^2 + 2*x*y + 3*x*z + x*w - x*t - x*u + 3*x*v + 4*y^2 + 4*y*z - 2*y*w - 4*y*t - 4*y*v - z^2 - 6*z*w + 3*z*t + 2*z*u + 2*z*v + 3*w^2 + 2*w*u + 2*w*v - 5*t^2 + t*u - t*v - 7*u^2 - 4*u*v + 3*v^2 - r*a + r*c + r*d + s*c + a*b - a*c - a*d - c*d, x^2 - 3*x*y + 3*x*z - 4*x*w + x*t - x*u + 2*x*v - 4*y^2 - y*z + 2*y*w - 2*y*t + y*u + 2*y*v - z^2 - z*w - 3*z*t + 3*z*u - 5*z*v + w^2 + w*t - 4*w*u + 3*w*v - 7*t^2 + 2*t*u + t*v + 4*u^2 + 2*v^2 + r^2 + r*s - 2*r*a - r*b - s^2 - s*a - a^2 - a*c - 2*a*d - b*d, x^2 - 2*x*y - 4*x*z + 2*x*w + 2*x*t - 5*x*u + 2*x*v - y^2 - 3*y*z + y*w + 5*y*t - 2*y*u + 4*z^2 - 2*z*w - 3*z*u + z*v - 2*w^2 + w*t - w*u + 3*w*v + 2*t^2 - t*u - 3*t*v + 4*u^2 + 3*u*v + 5*v^2 - r*s - r*a - r*c - a*b + a*c, 3*x^2 + x*y + 5*x*z + 3*x*t - 2*x*v - 2*y^2 + 2*y*w + 2*y*u - 6*y*v - z^2 - 3*z*w + 3*z*t + 2*z*u + 2*z*v + w^2 - 3*w*t + 5*w*u + w*v + 4*t^2 + 7*t*u + 3*t*v + 5*u^2 + 2*u*v - 2*v^2 + r*a - s*c - a*c, 5*x^2 + 4*x*y + 5*x*z + x*w - 2*x*t - 3*x*u - x*v - y*z + 3*y*w + y*t - 3*y*u + y*v - 2*z^2 - 6*z*w + 3*z*t + 2*z*u + 6*z*v + 2*w^2 + 2*w*t - 3*w*u + 3*w*v + 2*t^2 + 2*t*u + t*v - 2*u^2 - 3*u*v - 5*v^2 + r*a + r*b, 2*x^2 + 3*x*z + 2*x*w - 2*x*t - x*v + 2*y^2 - 2*y*z - 2*y*w - 4*y*t + 3*y*u + y*v + 5*z^2 - 2*z*w + 5*z*t + 3*z*u - 3*w^2 - 3*w*t + 7*w*u + 4*w*v - 4*t*v + 2*u*v - 4*v^2 - r^2 + r*a + r*c + a^2 + a*b - a*c, 2*x^2 + 4*x*y + 2*x*z - 2*x*t + x*v + 7*y^2 + 3*y*z - y*w + 2*y*t - 4*y*u + 2*z^2 - 3*z*w + z*t + z*u + 3*z*v + 7*w^2 - w*t - 2*w*u - 2*w*v - t*v + 6*u*v - r^2 - 2*r*a - r*c - s*a + s*c - s*d - a^2 - a*d + d^2, 6*x^2 - 2*x*y + x*z - 4*x*w + 7*x*t + x*v - 2*y^2 + y*z + 3*y*w + 5*y*t - y*u + 3*y*v + 2*z^2 - 2*z*w + 2*z*t - 2*z*u - 5*z*v - w^2 - 4*w*t - 3*w*u - 4*w*v - 3*t^2 - 3*t*u - t*v + 3*u^2 + u*v - v^2 - r*c - r*d]

Singular plane model Singular plane model

$ 0 $

$=$

$ 6561 x^{8} y^{16} + 87480 x^{8} y^{14} z^{2} + 451980 x^{8} y^{12} z^{4} + 1117800 x^{8} y^{10} z^{6} + \cdots + 45796 z^{24} $

[6561*x^8*y^16 + 87480*x^8*y^14*z^2 + 451980*x^8*y^12*z^4 + 1117800*x^8*y^10*z^6 + 1308150*x^8*y^8*z^8 + 621000*x^8*y^6*z^10 + 139500*x^8*y^4*z^12 + 15000*x^8*y^2*z^14 + 625*x^8*z^16 + 26244*x^7*y^16*z + 349920*x^7*y^14*z^3 + 1807920*x^7*y^12*z^5 + 4471200*x^7*y^10*z^7 + 5232600*x^7*y^8*z^9 + 2484000*x^7*y^6*z^11 + 558000*x^7*y^4*z^13 + 60000*x^7*y^2*z^15 + 2500*x^7*z^17 + 118098*x^6*y^18 + 1167858*x^6*y^16*z^2 + 3341736*x^6*y^14*z^4 - 1393848*x^6*y^12*z^6 - 21612420*x^6*y^10*z^8 - 32252580*x^6*y^8*z^10 - 13635000*x^6*y^6*z^12 - 2352600*x^6*y^4*z^14 - 162750*x^6*y^2*z^16 - 2750*x^6*z^18 + 472392*x^5*y^18*z + 5616216*x^5*y^16*z^3 + 25404192*x^5*y^14*z^5 + 51858144*x^5*y^12*z^7 + 37873008*x^5*y^10*z^9 - 15390000*x^5*y^8*z^11 - 26736480*x^5*y^6*z^13 - 7927200*x^5*y^4*z^15 - 775800*x^5*y^2*z^17 - 17000*x^5*z^19 + 1240029*x^4*y^20 + 12872682*x^4*y^18*z^2 + 50709969*x^4*y^16*z^4 + 107023032*x^4*y^14*z^6 + 195530922*x^4*y^12*z^8 + 368649468*x^4*y^10*z^10 + 393957594*x^4*y^8*z^12 + 129946680*x^4*y^6*z^14 + 16614585*x^4*y^4*z^16 + 772650*x^4*y^2*z^18 + 8725*x^4*z^20 + 708588*x^3*y^20*z - 3306744*x^3*y^18*z^3 - 95239476*x^3*y^16*z^5 - 513332640*x^3*y^14*z^7 - 1212105384*x^3*y^12*z^9 - 1321916112*x^3*y^10*z^11 - 517612680*x^3*y^8*z^13 + 24725088*x^3*y^6*z^15 + 30236220*x^3*y^4*z^17 + 3089160*x^3*y^2*z^19 + 48700*x^3*z^21 + 7794468*x^2*y^22 + 95423184*x^2*y^20*z^2 + 498767220*x^2*y^18*z^4 + 1482628536*x^2*y^16*z^6 + 2705633928*x^2*y^14*z^8 + 2703808512*x^2*y^12*z^10 + 613936584*x^2*y^10*z^12 - 948110832*x^2*y^8*z^14 - 290751660*x^2*y^6*z^16 - 48293136*x^2*y^4*z^18 - 2488380*x^2*y^2*z^20 - 28040*x^2*z^22 - 7085880*x*y^22*z - 127073448*x*y^20*z^3 - 808577640*x*y^18*z^5 - 2298082104*x*y^16*z^7 - 2600640432*x*y^14*z^9 + 341603568*x*y^12*z^11 + 2436162480*x*y^10*z^13 + 868673808*x*y^8*z^15 + 105717096*x*y^6*z^17 - 49140936*x*y^4*z^19 - 3774408*x*y^2*z^21 - 55640*x*z^23 + 19131876*y^24 + 235251216*y^22*z^2 + 1156888008*y^20*z^4 + 2815141392*y^18*z^6 + 3274175196*y^16*z^8 + 1122753312*y^14*z^10 - 606819600*y^12*z^12 - 49027680*y^10*z^14 + 228243420*y^8*z^16 + 144346320*y^6*z^18 + 65893320*y^4*z^20 + 3311184*y^2*z^22 + 45796*z^24]

Rational points

This modular curve has no real points and no $\Q_p$ points for $p=7$, 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 30.120.7.h.1 :

$\displaystyle X$	$=$	$\displaystyle -x$
$\displaystyle Y$	$=$	$\displaystyle -y$
$\displaystyle Z$	$=$	$\displaystyle -z$
$\displaystyle W$	$=$	$\displaystyle u$
$\displaystyle T$	$=$	$\displaystyle -w$
$\displaystyle U$	$=$	$\displaystyle -t$
$\displaystyle V$	$=$	$\displaystyle v$

Equation of the image curve:

$0$	$=$	$ XY-2Y^{2}+YZ+Z^{2}-XW+YW-YT+YV-WV $
	$=$	$ 2X^{2}+XY-2XZ-2Z^{2}+2XW-YW+ZW+W^{2}+XT-YT+WT-XU-YU+ZU+WU-TU-U^{2}-ZV $
	$=$	$ X^{2}-3XZ+YZ+Z^{2}+2XW-2ZW-XT-WT-T^{2}-XU+YU-3ZU-2TU+XV+YV-WV-UV $
	$=$	$ X^{2}-XY-3YZ+YW-2ZW-YT-ZT-WT-T^{2}-XU-3ZU-2TU+XV-YV+TV-UV $
	$=$	$ 2XZ+YZ+2XW-2YW+ZW+2XT-2YT+ZT+WT+T^{2}+YU+2ZU+TU+YV+ZV-WV $
	$=$	$ 2XY+2XZ+Z^{2}+2XW-ZW+XT+2ZT-WT+YU-2ZU-TU-WV $
	$=$	$ X^{2}-XZ+YZ+XW-2YW+ZW+XT-2ZT-WT-XU+2YU+TU+XV-YV+2ZV+WV-TV-UV $
	$=$	$ 2XY-3XZ-2YZ-2Z^{2}-XW-ZW-2XT-2YT-2ZT-T^{2}+YU-ZU-TU-ZV-WV $
	$=$	$ 2X^{2}-2XZ+YZ-Z^{2}-XW-XT+2ZT+T^{2}-2XU+2YU-2XV+YV-3ZV-WV-2TV+2UV $
	$=$	$ X^{2}-XZ+YZ-2YW-W^{2}+3XT-2YT-ZT+T^{2}+3XU+YU+ZU-WU+2TU+U^{2}-4XV+YV-WV-TV-UV-V^{2} $

Map of degree 1 from the canonical model of this modular curve to the plane model of the modular curve 60.240.13.nl.1 :

$\displaystyle X$	$=$	$\displaystyle d$
$\displaystyle Y$	$=$	$\displaystyle \frac{5}{2}x$
$\displaystyle Z$	$=$	$\displaystyle \frac{1}{2}r$

Equation of the image curve:

$0$

$=$

$ 6561X^{8}Y^{16}+118098X^{6}Y^{18}+1240029X^{4}Y^{20}+7794468X^{2}Y^{22}+19131876Y^{24}+26244X^{7}Y^{16}Z+472392X^{5}Y^{18}Z+708588X^{3}Y^{20}Z-7085880XY^{22}Z+87480X^{8}Y^{14}Z^{2}+1167858X^{6}Y^{16}Z^{2}+12872682X^{4}Y^{18}Z^{2}+95423184X^{2}Y^{20}Z^{2}+235251216Y^{22}Z^{2}+349920X^{7}Y^{14}Z^{3}+5616216X^{5}Y^{16}Z^{3}-3306744X^{3}Y^{18}Z^{3}-127073448XY^{20}Z^{3}+451980X^{8}Y^{12}Z^{4}+3341736X^{6}Y^{14}Z^{4}+50709969X^{4}Y^{16}Z^{4}+498767220X^{2}Y^{18}Z^{4}+1156888008Y^{20}Z^{4}+1807920X^{7}Y^{12}Z^{5}+25404192X^{5}Y^{14}Z^{5}-95239476X^{3}Y^{16}Z^{5}-808577640XY^{18}Z^{5}+1117800X^{8}Y^{10}Z^{6}-1393848X^{6}Y^{12}Z^{6}+107023032X^{4}Y^{14}Z^{6}+1482628536X^{2}Y^{16}Z^{6}+2815141392Y^{18}Z^{6}+4471200X^{7}Y^{10}Z^{7}+51858144X^{5}Y^{12}Z^{7}-513332640X^{3}Y^{14}Z^{7}-2298082104XY^{16}Z^{7}+1308150X^{8}Y^{8}Z^{8}-21612420X^{6}Y^{10}Z^{8}+195530922X^{4}Y^{12}Z^{8}+2705633928X^{2}Y^{14}Z^{8}+3274175196Y^{16}Z^{8}+5232600X^{7}Y^{8}Z^{9}+37873008X^{5}Y^{10}Z^{9}-1212105384X^{3}Y^{12}Z^{9}-2600640432XY^{14}Z^{9}+621000X^{8}Y^{6}Z^{10}-32252580X^{6}Y^{8}Z^{10}+368649468X^{4}Y^{10}Z^{10}+2703808512X^{2}Y^{12}Z^{10}+1122753312Y^{14}Z^{10}+2484000X^{7}Y^{6}Z^{11}-15390000X^{5}Y^{8}Z^{11}-1321916112X^{3}Y^{10}Z^{11}+341603568XY^{12}Z^{11}+139500X^{8}Y^{4}Z^{12}-13635000X^{6}Y^{6}Z^{12}+393957594X^{4}Y^{8}Z^{12}+613936584X^{2}Y^{10}Z^{12}-606819600Y^{12}Z^{12}+558000X^{7}Y^{4}Z^{13}-26736480X^{5}Y^{6}Z^{13}-517612680X^{3}Y^{8}Z^{13}+2436162480XY^{10}Z^{13}+15000X^{8}Y^{2}Z^{14}-2352600X^{6}Y^{4}Z^{14}+129946680X^{4}Y^{6}Z^{14}-948110832X^{2}Y^{8}Z^{14}-49027680Y^{10}Z^{14}+60000X^{7}Y^{2}Z^{15}-7927200X^{5}Y^{4}Z^{15}+24725088X^{3}Y^{6}Z^{15}+868673808XY^{8}Z^{15}+625X^{8}Z^{16}-162750X^{6}Y^{2}Z^{16}+16614585X^{4}Y^{4}Z^{16}-290751660X^{2}Y^{6}Z^{16}+228243420Y^{8}Z^{16}+2500X^{7}Z^{17}-775800X^{5}Y^{2}Z^{17}+30236220X^{3}Y^{4}Z^{17}+105717096XY^{6}Z^{17}-2750X^{6}Z^{18}+772650X^{4}Y^{2}Z^{18}-48293136X^{2}Y^{4}Z^{18}+144346320Y^{6}Z^{18}-17000X^{5}Z^{19}+3089160X^{3}Y^{2}Z^{19}-49140936XY^{4}Z^{19}+8725X^{4}Z^{20}-2488380X^{2}Y^{2}Z^{20}+65893320Y^{4}Z^{20}+48700X^{3}Z^{21}-3774408XY^{2}Z^{21}-28040X^{2}Z^{22}+3311184Y^{2}Z^{22}-55640XZ^{23}+45796Z^{24} $

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
60.240.7-30.h.1.10	$60$	$2$	$2$	$7$	$0$	$1^{6}$
60.240.7-30.h.1.14	$60$	$2$	$2$	$7$	$0$	$1^{6}$

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
60.960.29-60.bh.1.10	$60$	$2$	$2$	$29$	$0$	$1^{16}$
60.960.29-60.eg.1.20	$60$	$2$	$2$	$29$	$4$	$1^{16}$
60.960.29-60.fl.1.1	$60$	$2$	$2$	$29$	$4$	$1^{16}$
60.960.29-60.fn.1.7	$60$	$2$	$2$	$29$	$0$	$1^{16}$
60.960.29-60.la.1.14	$60$	$2$	$2$	$29$	$8$	$1^{16}$
60.960.29-60.lc.1.14	$60$	$2$	$2$	$29$	$9$	$1^{16}$
60.960.29-60.ld.1.5	$60$	$2$	$2$	$29$	$9$	$1^{16}$
60.960.29-60.lg.1.3	$60$	$2$	$2$	$29$	$8$	$1^{16}$
60.960.29-60.mz.1.12	$60$	$2$	$2$	$29$	$4$	$1^{16}$
60.960.29-60.nb.1.11	$60$	$2$	$2$	$29$	$5$	$1^{16}$
60.960.29-60.nd.1.8	$60$	$2$	$2$	$29$	$5$	$1^{16}$
60.960.29-60.nf.1.2	$60$	$2$	$2$	$29$	$4$	$1^{16}$
60.960.29-60.nn.1.15	$60$	$2$	$2$	$29$	$4$	$1^{16}$
60.960.29-60.np.1.14	$60$	$2$	$2$	$29$	$2$	$1^{16}$
60.960.29-60.nr.1.4	$60$	$2$	$2$	$29$	$2$	$1^{16}$
60.960.29-60.nt.1.6	$60$	$2$	$2$	$29$	$4$	$1^{16}$
60.960.33-60.pe.1.11	$60$	$2$	$2$	$33$	$7$	$1^{20}$
60.960.33-60.pg.1.13	$60$	$2$	$2$	$33$	$8$	$1^{20}$
60.960.33-60.pu.1.15	$60$	$2$	$2$	$33$	$7$	$1^{20}$
60.960.33-60.pw.1.9	$60$	$2$	$2$	$33$	$6$	$1^{20}$
60.960.33-60.qf.1.14	$60$	$2$	$2$	$33$	$4$	$1^{20}$
60.960.33-60.qi.1.12	$60$	$2$	$2$	$33$	$3$	$1^{20}$
60.960.33-60.qo.1.10	$60$	$2$	$2$	$33$	$12$	$1^{20}$
60.960.33-60.qq.1.24	$60$	$2$	$2$	$33$	$9$	$1^{20}$
60.1440.37-60.nn.1.29	$60$	$3$	$3$	$37$	$9$	$1^{24}$
60.1440.45-60.j.1.9	$60$	$3$	$3$	$45$	$11$	$1^{28}\cdot2^{2}$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi
Siegel

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Modular curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Galois groups
Sato-Tate groups
Abstract groups
Lattices

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Motives

Groups

Database

Properties

Related objects

Downloads

Learn more