Modular curve 248.48.0.g.2

• Label: 248.48.0.g.2
• Level: $248$
• Index: $48$
• Genus: $0$
• Cusps: $10$
• $\Q$-cusps: $0$

Invariants

Level:	$248$		$\SL_2$-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	$4^{8}\cdot8^{2}$		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:

8N0

Level structure

$\GL_2(\Z/248\Z)$-generators:	$\begin{bmatrix}3&58\\140&211\end{bmatrix}$, $\begin{bmatrix}63&6\\16&117\end{bmatrix}$, $\begin{bmatrix}163&94\\200&67\end{bmatrix}$, $\begin{bmatrix}165&98\\200&161\end{bmatrix}$, $\begin{bmatrix}211&172\\12&25\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	248.96.0-248.g.2.1, 248.96.0-248.g.2.2, 248.96.0-248.g.2.3, 248.96.0-248.g.2.4, 248.96.0-248.g.2.5, 248.96.0-248.g.2.6, 248.96.0-248.g.2.7, 248.96.0-248.g.2.8, 248.96.0-248.g.2.9, 248.96.0-248.g.2.10, 248.96.0-248.g.2.11, 248.96.0-248.g.2.12, 248.96.0-248.g.2.13, 248.96.0-248.g.2.14, 248.96.0-248.g.2.15, 248.96.0-248.g.2.16
Cyclic 248-isogeny field degree:	$64$
Cyclic 248-torsion field degree:	$7680$
Full 248-torsion field degree:	$28569600$

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	$8$	$2$	$2$	$0$	$0$
124.24.0.c.1	$124$	$2$	$2$	$0$	$?$
248.24.0.h.2	$248$	$2$	$2$	$0$	$?$

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

Covering curve	Level	Index	Degree	Genus
248.96.1.c.1	$248$	$2$	$2$	$1$
248.96.1.i.2	$248$	$2$	$2$	$1$
248.96.1.ba.2	$248$	$2$	$2$	$1$
248.96.1.bc.1	$248$	$2$	$2$	$1$
248.96.1.bs.2	$248$	$2$	$2$	$1$
248.96.1.bu.1	$248$	$2$	$2$	$1$
248.96.1.ca.1	$248$	$2$	$2$	$1$
248.96.1.cb.2	$248$	$2$	$2$	$1$