Modular curve 312.24.0.ds.1

• Label: 312.24.0.ds.1
• Level: $312$
• Index: $24$
• Genus: $0$
• Cusps: $6$
• $\Q$-cusps: $0$

Invariants

Level:	$312$		$\SL_2$-level:	$8$
Index:	$24$		$\PSL_2$-index:	$24$
Genus:	$0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps:	$6$ (none of which are rational)		Cusp widths	$2^{4}\cdot8^{2}$		Cusp orbits	$2^{3}$
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:

8G0

Level structure

$\GL_2(\Z/312\Z)$-generators:	$\begin{bmatrix}79&200\\266&299\end{bmatrix}$, $\begin{bmatrix}125&208\\280&193\end{bmatrix}$, $\begin{bmatrix}235&136\\203&169\end{bmatrix}$, $\begin{bmatrix}273&148\\64&29\end{bmatrix}$, $\begin{bmatrix}287&32\\184&237\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	312.48.0-312.ds.1.1, 312.48.0-312.ds.1.2, 312.48.0-312.ds.1.3, 312.48.0-312.ds.1.4, 312.48.0-312.ds.1.5, 312.48.0-312.ds.1.6, 312.48.0-312.ds.1.7, 312.48.0-312.ds.1.8, 312.48.0-312.ds.1.9, 312.48.0-312.ds.1.10, 312.48.0-312.ds.1.11, 312.48.0-312.ds.1.12, 312.48.0-312.ds.1.13, 312.48.0-312.ds.1.14, 312.48.0-312.ds.1.15, 312.48.0-312.ds.1.16
Cyclic 312-isogeny field degree:	$112$
Cyclic 312-torsion field degree:	$10752$
Full 312-torsion field degree:	$80510976$

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
24.12.0.ba.1	$24$	$2$	$2$	$0$	$0$
104.12.0.z.1	$104$	$2$	$2$	$0$	$?$
156.12.0.g.1	$156$	$2$	$2$	$0$	$?$

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

Covering curve	Level	Index	Degree	Genus
312.72.4.ng.1	$312$	$3$	$3$	$4$
312.96.3.py.1	$312$	$4$	$4$	$3$
312.336.23.jr.1	$312$	$14$	$14$	$23$