LMFDB - Modular curve 280.504.13-28.a.1.2

Invariants

Level:	$280$	$\SL_2$-level:	$28$	Newform level:	$784$
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	$6^{3}$
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:	$\begin{bmatrix}11&238\\16&157\end{bmatrix}$, $\begin{bmatrix}41&38\\200&183\end{bmatrix}$, $\begin{bmatrix}51&266\\78&61\end{bmatrix}$, $\begin{bmatrix}87&138\\58&109\end{bmatrix}$, $\begin{bmatrix}131&226\\214&167\end{bmatrix}$, $\begin{bmatrix}229&274\\142&121\end{bmatrix}$
Contains $-I$:	no $\quad$ (see 28.252.13.a.1 for the level structure with $-I$)
Cyclic 280-isogeny field degree:	$192$
Cyclic 280-torsion field degree:	$18432$
Full 280-torsion field degree:	$2949120$

Models

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

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

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

Singular plane model Singular plane model

$ 0 $

$=$

$ - 78124583152 x^{18} y^{6} - 468747498912 x^{18} y^{5} z - 1171868747280 x^{18} y^{4} z^{2} + \cdots + 14220441 z^{24} $

[-78124583152*x^18*y^6 - 468747498912*x^18*y^5*z - 1171868747280*x^18*y^4*z^2 - 1562491663040*x^18*y^3*z^3 - 1171868747280*x^18*y^2*z^4 - 468747498912*x^18*y*z^5 - 78124583152*x^18*z^6 - 3622324237952*x^16*y^8 - 15474201673056*x^16*y^7*z - 17561889766400*x^16*y^6*z^2 + 16022457307360*x^16*y^5*z^3 + 55952697321920*x^16*y^4*z^4 + 51095322117728*x^16*y^3*z^5 + 17689545519744*x^16*y^2*z^6 - 238893353440*x^16*y*z^7 - 1053344438720*x^16*z^8 - 57385859792240*x^14*y^10 - 232287141851072*x^14*y^9*z - 262989935027036*x^14*y^8*z^2 + 80781708405608*x^14*y^7*z^3 + 326518661351372*x^14*y^6*z^4 + 137515948034528*x^14*y^5*z^5 - 119736837272276*x^14*y^4*z^6 - 251360984093688*x^14*y^3*z^7 - 278555398441180*x^14*y^2*z^8 - 163108726073104*x^14*y*z^9 - 36309826396368*x^14*z^10 + 83979649170760*x^12*y^12 + 241025826272280*x^12*y^11*z + 542015426989337*x^12*y^10*z^2 + 877830182311964*x^12*y^9*z^3 + 744572070177628*x^12*y^8*z^4 + 752275234454212*x^12*y^7*z^5 + 571958819517750*x^12*y^6*z^6 - 764229725347116*x^12*y^5*z^7 - 1169216242808516*x^12*y^4*z^8 + 97765991935780*x^12*y^3*z^9 + 888963229651273*x^12*y^2*z^10 + 627338111849232*x^12*y*z^11 + 169747245959816*x^12*z^12 - 39752074453028*x^10*y^14 - 40586410236148*x^10*y^13*z - 408283756167462*x^10*y^12*z^2 - 906589776333234*x^10*y^11*z^3 - 1632458194813264*x^10*y^10*z^4 - 1806605700670288*x^10*y^9*z^5 - 930083734699840*x^10*y^8*z^6 - 2634924274592008*x^10*y^7*z^7 - 3822185881900428*x^10*y^6*z^8 + 504059999541840*x^10*y^5*z^9 + 3167849975250394*x^10*y^4*z^10 + 809498888040682*x^10*y^3*z^11 - 415005940728736*x^10*y^2*z^12 - 82867902087740*x^10*y*z^13 - 75632403746004*x^10*z^14 + 8774856773144*x^8*y^16 - 7632496210220*x^8*y^15*z + 147809084190201*x^8*y^14*z^2 + 147029027802076*x^8*y^13*z^3 + 958126342929455*x^8*y^12*z^4 + 1036275504818330*x^8*y^11*z^5 + 1045828773162544*x^8*y^10*z^6 + 3093261602151980*x^8*y^9*z^7 + 5844291029724714*x^8*y^8*z^8 + 1623426440855408*x^8*y^7*z^9 - 4778697124452475*x^8*y^6*z^10 - 879956745630172*x^8*y^5*z^11 + 1344809314344111*x^8*y^4*z^12 - 479406184371646*x^8*y^3*z^13 + 53510898343826*x^8*y^2*z^14 + 4083171303988*x^8*y*z^15 + 13478629231648*x^8*z^16 - 983406037971*x^6*y^18 + 2341977412698*x^6*y^17*z - 24935667145662*x^6*y^16*z^2 + 20262321744504*x^6*y^15*z^3 - 239194774744702*x^6*y^14*z^4 - 108864234981054*x^6*y^13*z^5 - 721886186109557*x^6*y^12*z^6 - 457993606867580*x^6*y^11*z^7 - 2268423122659274*x^6*y^10*z^8 - 2094996064904162*x^6*y^9*z^9 + 1924919293076801*x^6*y^8*z^10 + 683543707689304*x^6*y^7*z^11 - 875250089125454*x^6*y^6*z^12 + 368647278000750*x^6*y^5*z^13 + 35148238712909*x^6*y^4*z^14 - 36203429825556*x^6*y^3*z^15 + 13550699622985*x^6*y^2*z^16 - 1785296524648*x^6*y*z^17 - 1229979405627*x^6*z^18 + 53701626538*x^4*y^20 - 151226960108*x^4*y^19*z + 1847619340644*x^4*y^18*z^2 - 4079633634426*x^4*y^17*z^3 + 22842494786461*x^4*y^16*z^4 - 27717181602110*x^4*y^15*z^5 + 165584736832921*x^4*y^14*z^6 - 86776064308080*x^4*y^13*z^7 + 371848758302315*x^4*y^12*z^8 + 494624012412838*x^4*y^11*z^9 - 106229436404819*x^4*y^10*z^10 - 276273997941256*x^4*y^9*z^11 + 70031022493761*x^4*y^8*z^12 + 83845230068446*x^4*y^7*z^13 - 9118184690405*x^4*y^6*z^14 - 3329796602104*x^4*y^5*z^15 + 3961456623607*x^4*y^4*z^16 - 1267599542874*x^4*y^3*z^17 - 793419772005*x^4*y^2*z^18 + 167352427242*x^4*y*z^19 + 64319831478*x^4*z^20 - 1166318475*x^2*y^22 + 226319338*x^2*y^21*z - 53999655577*x^2*y^20*z^2 + 246038082738*x^2*y^19*z^3 - 1260044428762*x^2*y^18*z^4 + 3381390786774*x^2*y^17*z^5 - 8535459679999*x^2*y^16*z^6 + 8684938092096*x^2*y^15*z^7 - 947704877882*x^2*y^14*z^8 - 13981265427976*x^2*y^13*z^9 + 5072355894214*x^2*y^12*z^10 + 51588162009524*x^2*y^11*z^11 + 22225463215032*x^2*y^10*z^12 - 30137982569968*x^2*y^9*z^13 - 13451420723230*x^2*y^8*z^14 + 8864338873264*x^2*y^7*z^15 + 3692263244509*x^2*y^6*z^16 - 1213468881618*x^2*y^5*z^17 - 393960159901*x^2*y^4*z^18 + 130111783466*x^2*y^3*z^19 + 26586386442*x^2*y^2*z^20 - 8598321270*x^2*y*z^21 - 1726241139*x^2*z^22 + 4198401*y^24 + 116936430*y^23*z + 375358621*y^22*z^2 - 4722987898*y^21*z^3 + 29363852928*y^20*z^4 - 95573622758*y^19*z^5 + 155412836549*y^18*z^6 - 49051120506*y^17*z^7 - 442214526045*y^16*z^8 + 796807035764*y^15*z^9 + 514851646194*y^14*z^10 - 1620052975532*y^13*z^11 - 737001610788*y^12*z^12 + 1483996895084*y^11*z^13 + 1031997803090*y^10*z^14 - 301345204652*y^9*z^15 - 363854314701*y^8*z^16 + 18283231486*y^7*z^17 + 75947663713*y^6*z^18 + 8889789542*y^5*z^19 - 7643585612*y^4*z^20 - 1688189670*y^3*z^21 + 383710329*y^2*z^22 + 158630886*y*z^23 + 14220441*z^24]

Rational points

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

Map of degree 3 from the canonical model of this modular curve to the canonical model of the modular curve 28.84.5.a.1 :

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

Equation of the image curve:

$0$	$=$	$ 3X^{2}-6XY-4Y^{2}+4XZ+3YZ-Z^{2} $
	$=$	$ X^{2}-2XY+Y^{2}-XZ+8YZ-5Z^{2}+W^{2} $
	$=$	$ 39X^{2}+6XY-3Y^{2}-32XZ+4YZ+15Z^{2}+2W^{2}-T^{2} $

Map of degree 1 from the canonical model of this modular curve to the plane model of the modular curve 28.252.13.a.1 :

$\displaystyle X$	$=$	$\displaystyle b$
$\displaystyle Y$	$=$	$\displaystyle 7x$
$\displaystyle Z$	$=$	$\displaystyle 7y$

Equation of the image curve:

$0$

$=$

$ -78124583152X^{18}Y^{6}-468747498912X^{18}Y^{5}Z-1171868747280X^{18}Y^{4}Z^{2}-1562491663040X^{18}Y^{3}Z^{3}-1171868747280X^{18}Y^{2}Z^{4}-468747498912X^{18}YZ^{5}-78124583152X^{18}Z^{6}-3622324237952X^{16}Y^{8}-15474201673056X^{16}Y^{7}Z-17561889766400X^{16}Y^{6}Z^{2}+16022457307360X^{16}Y^{5}Z^{3}+55952697321920X^{16}Y^{4}Z^{4}+51095322117728X^{16}Y^{3}Z^{5}+17689545519744X^{16}Y^{2}Z^{6}-238893353440X^{16}YZ^{7}-1053344438720X^{16}Z^{8}-57385859792240X^{14}Y^{10}-232287141851072X^{14}Y^{9}Z-262989935027036X^{14}Y^{8}Z^{2}+80781708405608X^{14}Y^{7}Z^{3}+326518661351372X^{14}Y^{6}Z^{4}+137515948034528X^{14}Y^{5}Z^{5}-119736837272276X^{14}Y^{4}Z^{6}-251360984093688X^{14}Y^{3}Z^{7}-278555398441180X^{14}Y^{2}Z^{8}-163108726073104X^{14}YZ^{9}-36309826396368X^{14}Z^{10}+83979649170760X^{12}Y^{12}+241025826272280X^{12}Y^{11}Z+542015426989337X^{12}Y^{10}Z^{2}+877830182311964X^{12}Y^{9}Z^{3}+744572070177628X^{12}Y^{8}Z^{4}+752275234454212X^{12}Y^{7}Z^{5}+571958819517750X^{12}Y^{6}Z^{6}-764229725347116X^{12}Y^{5}Z^{7}-1169216242808516X^{12}Y^{4}Z^{8}+97765991935780X^{12}Y^{3}Z^{9}+888963229651273X^{12}Y^{2}Z^{10}+627338111849232X^{12}YZ^{11}+169747245959816X^{12}Z^{12}-39752074453028X^{10}Y^{14}-40586410236148X^{10}Y^{13}Z-408283756167462X^{10}Y^{12}Z^{2}-906589776333234X^{10}Y^{11}Z^{3}-1632458194813264X^{10}Y^{10}Z^{4}-1806605700670288X^{10}Y^{9}Z^{5}-930083734699840X^{10}Y^{8}Z^{6}-2634924274592008X^{10}Y^{7}Z^{7}-3822185881900428X^{10}Y^{6}Z^{8}+504059999541840X^{10}Y^{5}Z^{9}+3167849975250394X^{10}Y^{4}Z^{10}+809498888040682X^{10}Y^{3}Z^{11}-415005940728736X^{10}Y^{2}Z^{12}-82867902087740X^{10}YZ^{13}-75632403746004X^{10}Z^{14}+8774856773144X^{8}Y^{16}-7632496210220X^{8}Y^{15}Z+147809084190201X^{8}Y^{14}Z^{2}+147029027802076X^{8}Y^{13}Z^{3}+958126342929455X^{8}Y^{12}Z^{4}+1036275504818330X^{8}Y^{11}Z^{5}+1045828773162544X^{8}Y^{10}Z^{6}+3093261602151980X^{8}Y^{9}Z^{7}+5844291029724714X^{8}Y^{8}Z^{8}+1623426440855408X^{8}Y^{7}Z^{9}-4778697124452475X^{8}Y^{6}Z^{10}-879956745630172X^{8}Y^{5}Z^{11}+1344809314344111X^{8}Y^{4}Z^{12}-479406184371646X^{8}Y^{3}Z^{13}+53510898343826X^{8}Y^{2}Z^{14}+4083171303988X^{8}YZ^{15}+13478629231648X^{8}Z^{16}-983406037971X^{6}Y^{18}+2341977412698X^{6}Y^{17}Z-24935667145662X^{6}Y^{16}Z^{2}+20262321744504X^{6}Y^{15}Z^{3}-239194774744702X^{6}Y^{14}Z^{4}-108864234981054X^{6}Y^{13}Z^{5}-721886186109557X^{6}Y^{12}Z^{6}-457993606867580X^{6}Y^{11}Z^{7}-2268423122659274X^{6}Y^{10}Z^{8}-2094996064904162X^{6}Y^{9}Z^{9}+1924919293076801X^{6}Y^{8}Z^{10}+683543707689304X^{6}Y^{7}Z^{11}-875250089125454X^{6}Y^{6}Z^{12}+368647278000750X^{6}Y^{5}Z^{13}+35148238712909X^{6}Y^{4}Z^{14}-36203429825556X^{6}Y^{3}Z^{15}+13550699622985X^{6}Y^{2}Z^{16}-1785296524648X^{6}YZ^{17}-1229979405627X^{6}Z^{18}+53701626538X^{4}Y^{20}-151226960108X^{4}Y^{19}Z+1847619340644X^{4}Y^{18}Z^{2}-4079633634426X^{4}Y^{17}Z^{3}+22842494786461X^{4}Y^{16}Z^{4}-27717181602110X^{4}Y^{15}Z^{5}+165584736832921X^{4}Y^{14}Z^{6}-86776064308080X^{4}Y^{13}Z^{7}+371848758302315X^{4}Y^{12}Z^{8}+494624012412838X^{4}Y^{11}Z^{9}-106229436404819X^{4}Y^{10}Z^{10}-276273997941256X^{4}Y^{9}Z^{11}+70031022493761X^{4}Y^{8}Z^{12}+83845230068446X^{4}Y^{7}Z^{13}-9118184690405X^{4}Y^{6}Z^{14}-3329796602104X^{4}Y^{5}Z^{15}+3961456623607X^{4}Y^{4}Z^{16}-1267599542874X^{4}Y^{3}Z^{17}-793419772005X^{4}Y^{2}Z^{18}+167352427242X^{4}YZ^{19}+64319831478X^{4}Z^{20}-1166318475X^{2}Y^{22}+226319338X^{2}Y^{21}Z-53999655577X^{2}Y^{20}Z^{2}+246038082738X^{2}Y^{19}Z^{3}-1260044428762X^{2}Y^{18}Z^{4}+3381390786774X^{2}Y^{17}Z^{5}-8535459679999X^{2}Y^{16}Z^{6}+8684938092096X^{2}Y^{15}Z^{7}-947704877882X^{2}Y^{14}Z^{8}-13981265427976X^{2}Y^{13}Z^{9}+5072355894214X^{2}Y^{12}Z^{10}+51588162009524X^{2}Y^{11}Z^{11}+22225463215032X^{2}Y^{10}Z^{12}-30137982569968X^{2}Y^{9}Z^{13}-13451420723230X^{2}Y^{8}Z^{14}+8864338873264X^{2}Y^{7}Z^{15}+3692263244509X^{2}Y^{6}Z^{16}-1213468881618X^{2}Y^{5}Z^{17}-393960159901X^{2}Y^{4}Z^{18}+130111783466X^{2}Y^{3}Z^{19}+26586386442X^{2}Y^{2}Z^{20}-8598321270X^{2}YZ^{21}-1726241139X^{2}Z^{22}+4198401Y^{24}+116936430Y^{23}Z+375358621Y^{22}Z^{2}-4722987898Y^{21}Z^{3}+29363852928Y^{20}Z^{4}-95573622758Y^{19}Z^{5}+155412836549Y^{18}Z^{6}-49051120506Y^{17}Z^{7}-442214526045Y^{16}Z^{8}+796807035764Y^{15}Z^{9}+514851646194Y^{14}Z^{10}-1620052975532Y^{13}Z^{11}-737001610788Y^{12}Z^{12}+1483996895084Y^{11}Z^{13}+1031997803090Y^{10}Z^{14}-301345204652Y^{9}Z^{15}-363854314701Y^{8}Z^{16}+18283231486Y^{7}Z^{17}+75947663713Y^{6}Z^{18}+8889789542Y^{5}Z^{19}-7643585612Y^{4}Z^{20}-1688189670Y^{3}Z^{21}+383710329Y^{2}Z^{22}+158630886YZ^{23}+14220441Z^{24} $

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
280.252.7-14.a.1.2	$280$	$2$	$2$	$7$	$?$
280.252.7-14.a.1.4	$280$	$2$	$2$	$7$	$?$

Overview	Random
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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
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