Modular curve 104.48.0.r.2

• Label: 104.48.0.r.2
• Level: $104$
• Index: $48$
• Genus: $0$
• Cusps: $10$
• $\Q$-cusps: $0$

Invariants

Level:	$104$		$\SL_2$-level:	$8$
Index:	$48$		$\PSL_2$-index:	$48$
Genus:	$0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$
Cusps:	$10$ (none of which are rational)		Cusp widths	$2^{4}\cdot4^{2}\cdot8^{4}$		Cusp orbits	$2^{3}\cdot4$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
$\Q$-gonality:	$1 \le \gamma \le 2$
$\overline{\Q}$-gonality:	$1$
Rational cusps:	$0$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

8O0

Level structure

$\GL_2(\Z/104\Z)$-generators:	$\begin{bmatrix}29&4\\54&11\end{bmatrix}$, $\begin{bmatrix}73&72\\102&97\end{bmatrix}$, $\begin{bmatrix}87&28\\28&31\end{bmatrix}$, $\begin{bmatrix}89&56\\34&67\end{bmatrix}$, $\begin{bmatrix}91&36\\12&31\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	104.96.0-104.r.2.1, 104.96.0-104.r.2.2, 104.96.0-104.r.2.3, 104.96.0-104.r.2.4, 104.96.0-104.r.2.5, 104.96.0-104.r.2.6, 104.96.0-104.r.2.7, 104.96.0-104.r.2.8, 104.96.0-104.r.2.9, 104.96.0-104.r.2.10, 104.96.0-104.r.2.11, 104.96.0-104.r.2.12, 104.96.0-104.r.2.13, 104.96.0-104.r.2.14, 104.96.0-104.r.2.15, 104.96.0-104.r.2.16, 312.96.0-104.r.2.1, 312.96.0-104.r.2.2, 312.96.0-104.r.2.3, 312.96.0-104.r.2.4, 312.96.0-104.r.2.5, 312.96.0-104.r.2.6, 312.96.0-104.r.2.7, 312.96.0-104.r.2.8, 312.96.0-104.r.2.9, 312.96.0-104.r.2.10, 312.96.0-104.r.2.11, 312.96.0-104.r.2.12, 312.96.0-104.r.2.13, 312.96.0-104.r.2.14, 312.96.0-104.r.2.15, 312.96.0-104.r.2.16
Cyclic 104-isogeny field degree:	$28$
Cyclic 104-torsion field degree:	$1344$
Full 104-torsion field degree:	$838656$

Models

This modular curve is isomorphic to $\mathbb{P}^1$.

Rational points

This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
8.24.0.d.1	$8$	$2$	$2$	$0$	$0$
104.24.0.i.2	$104$	$2$	$2$	$0$	$?$
104.24.0.l.1	$104$	$2$	$2$	$0$	$?$

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

Covering curve	Level	Index	Degree	Genus
104.96.1.a.1	$104$	$2$	$2$	$1$
104.96.1.d.1	$104$	$2$	$2$	$1$
104.96.1.r.2	$104$	$2$	$2$	$1$
104.96.1.u.2	$104$	$2$	$2$	$1$
104.96.1.ba.2	$104$	$2$	$2$	$1$
104.96.1.bb.2	$104$	$2$	$2$	$1$
104.96.1.be.1	$104$	$2$	$2$	$1$
104.96.1.bf.1	$104$	$2$	$2$	$1$
312.96.1.ie.1	$312$	$2$	$2$	$1$
312.96.1.if.1	$312$	$2$	$2$	$1$
312.96.1.ik.1	$312$	$2$	$2$	$1$
312.96.1.il.1	$312$	$2$	$2$	$1$
312.96.1.jk.1	$312$	$2$	$2$	$1$
312.96.1.jl.1	$312$	$2$	$2$	$1$
312.96.1.jq.1	$312$	$2$	$2$	$1$
312.96.1.jr.1	$312$	$2$	$2$	$1$
312.144.8.ne.2	$312$	$3$	$3$	$8$
312.192.7.ho.1	$312$	$4$	$4$	$7$