Modular curve 228.240.17.b.1

• Label: 228.240.17.b.1
• Level: $228$
• Index: $240$
• Genus: $17$
• Cusps: $8$
• $\Q$-cusps: $4$

Invariants

Level:	$228$		$\SL_2$-level:	$76$		Newform level:	$1$
Index:	$240$		$\PSL_2$-index:	$240$
Genus:	$17 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$
Cusps:	$8$ (of which $4$ are rational)		Cusp widths	$2^{2}\cdot4^{2}\cdot38^{2}\cdot76^{2}$		Cusp orbits	$1^{4}\cdot2^{2}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$4 \le \gamma \le 17$
$\overline{\Q}$-gonality:	$4 \le \gamma \le 17$
Rational cusps:	$4$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

76A17

Level structure

$\GL_2(\Z/228\Z)$-generators:	$\begin{bmatrix}49&152\\2&155\end{bmatrix}$, $\begin{bmatrix}107&190\\126&145\end{bmatrix}$, $\begin{bmatrix}111&38\\92&155\end{bmatrix}$, $\begin{bmatrix}115&152\\12&79\end{bmatrix}$, $\begin{bmatrix}189&190\\220&161\end{bmatrix}$, $\begin{bmatrix}215&38\\186&223\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	228.480.17-228.b.1.1, 228.480.17-228.b.1.2, 228.480.17-228.b.1.3, 228.480.17-228.b.1.4, 228.480.17-228.b.1.5, 228.480.17-228.b.1.6, 228.480.17-228.b.1.7, 228.480.17-228.b.1.8, 228.480.17-228.b.1.9, 228.480.17-228.b.1.10, 228.480.17-228.b.1.11, 228.480.17-228.b.1.12, 228.480.17-228.b.1.13, 228.480.17-228.b.1.14, 228.480.17-228.b.1.15, 228.480.17-228.b.1.16, 228.480.17-228.b.1.17, 228.480.17-228.b.1.18, 228.480.17-228.b.1.19, 228.480.17-228.b.1.20
Cyclic 228-isogeny field degree:	$8$
Cyclic 228-torsion field degree:	$576$
Full 228-torsion field degree:	$2363904$

Rational points

This modular curve has 4 rational cusps but no known non-cuspidal rational points.

Modular covers

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve	Level	Index	Degree	Genus	Rank
12.12.0.b.1	$12$	$20$	$20$	$0$	$0$
$X_0(19)$	$19$	$12$	$12$	$1$	$0$

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
12.12.0.b.1	$12$	$20$	$20$	$0$	$0$
38.120.8.a.1	$38$	$2$	$2$	$8$	$0$
228.120.8.c.1	$228$	$2$	$2$	$8$	$?$
228.120.9.e.1	$228$	$2$	$2$	$9$	$?$