Modular curve 24.24.0.bs.1

• Label: 24.24.0.bs.1
• Level: $24$
• Index: $24$
• Genus: $0$
• Analytic rank: $0$
• Cusps: $6$
• $\Q$-cusps: $0$

Invariants

Level:	$24$		$\SL_2$-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
Rouse, Sutherland, and Zureick-Brown (RSZB) label:	24.24.0.216

Level structure

$\GL_2(\Z/24\Z)$-generators:	$\begin{bmatrix}3&22\\16&1\end{bmatrix}$, $\begin{bmatrix}13&14\\16&7\end{bmatrix}$, $\begin{bmatrix}23&3\\12&7\end{bmatrix}$, $\begin{bmatrix}23&14\\8&9\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	24.48.0-24.bs.1.1, 24.48.0-24.bs.1.2, 24.48.0-24.bs.1.3, 24.48.0-24.bs.1.4, 24.48.0-24.bs.1.5, 24.48.0-24.bs.1.6, 24.48.0-24.bs.1.7, 24.48.0-24.bs.1.8, 48.48.0-24.bs.1.1, 48.48.0-24.bs.1.2, 48.48.0-24.bs.1.3, 48.48.0-24.bs.1.4, 120.48.0-24.bs.1.1, 120.48.0-24.bs.1.2, 120.48.0-24.bs.1.3, 120.48.0-24.bs.1.4, 120.48.0-24.bs.1.5, 120.48.0-24.bs.1.6, 120.48.0-24.bs.1.7, 120.48.0-24.bs.1.8, 168.48.0-24.bs.1.1, 168.48.0-24.bs.1.2, 168.48.0-24.bs.1.3, 168.48.0-24.bs.1.4, 168.48.0-24.bs.1.5, 168.48.0-24.bs.1.6, 168.48.0-24.bs.1.7, 168.48.0-24.bs.1.8, 240.48.0-24.bs.1.1, 240.48.0-24.bs.1.2, 240.48.0-24.bs.1.3, 240.48.0-24.bs.1.4, 264.48.0-24.bs.1.1, 264.48.0-24.bs.1.2, 264.48.0-24.bs.1.3, 264.48.0-24.bs.1.4, 264.48.0-24.bs.1.5, 264.48.0-24.bs.1.6, 264.48.0-24.bs.1.7, 264.48.0-24.bs.1.8, 312.48.0-24.bs.1.1, 312.48.0-24.bs.1.2, 312.48.0-24.bs.1.3, 312.48.0-24.bs.1.4, 312.48.0-24.bs.1.5, 312.48.0-24.bs.1.6, 312.48.0-24.bs.1.7, 312.48.0-24.bs.1.8
Cyclic 24-isogeny field degree:	$8$
Cyclic 24-torsion field degree:	$64$
Full 24-torsion field degree:	$3072$

Models

Smooth plane model Smooth plane model

$ 0 $

$=$

$ 3 x^{2} + 3 y^{2} - 16 z^{2} $

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

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This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
8.12.0.o.1	$8$	$2$	$2$	$0$	$0$
12.12.0.h.1	$12$	$2$	$2$	$0$	$0$
24.12.0.ba.1	$24$	$2$	$2$	$0$	$0$

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

Covering curve	Level	Index	Degree	Genus
24.72.4.ga.1	$24$	$3$	$3$	$4$
24.96.3.ga.1	$24$	$4$	$4$	$3$
48.48.1.bc.1	$48$	$2$	$2$	$1$
48.48.1.be.1	$48$	$2$	$2$	$1$
48.48.1.cq.1	$48$	$2$	$2$	$1$
48.48.1.cs.1	$48$	$2$	$2$	$1$
120.120.8.ec.1	$120$	$5$	$5$	$8$
120.144.7.dmd.1	$120$	$6$	$6$	$7$
120.240.15.kc.1	$120$	$10$	$10$	$15$
168.192.11.ii.1	$168$	$8$	$8$	$11$
240.48.1.cc.1	$240$	$2$	$2$	$1$
240.48.1.cd.1	$240$	$2$	$2$	$1$
240.48.1.dy.1	$240$	$2$	$2$	$1$
240.48.1.dz.1	$240$	$2$	$2$	$1$
264.288.19.yt.1	$264$	$12$	$12$	$19$
312.336.23.hj.1	$312$	$14$	$14$	$23$