Modular curve 304.96.3.fi.1

• Label: 304.96.3.fi.1
• Level: $304$
• Index: $96$
• Genus: $3$
• Cusps: $12$
• $\Q$-cusps: $4$

Invariants

Level:	$304$		$\SL_2$-level:	$16$		Newform level:	$1$
Index:	$96$		$\PSL_2$-index:	$96$
Genus:	$3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$
Cusps:	$12$ (of which $4$ are rational)		Cusp widths	$4^{8}\cdot16^{4}$		Cusp orbits	$1^{4}\cdot2^{2}\cdot4$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$2 \le \gamma \le 3$
$\overline{\Q}$-gonality:	$2 \le \gamma \le 3$
Rational cusps:	$4$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

16I3

Level structure

$\GL_2(\Z/304\Z)$-generators:	$\begin{bmatrix}5&200\\96&89\end{bmatrix}$, $\begin{bmatrix}9&64\\166&149\end{bmatrix}$, $\begin{bmatrix}145&288\\219&23\end{bmatrix}$, $\begin{bmatrix}211&280\\253&141\end{bmatrix}$, $\begin{bmatrix}217&272\\287&155\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	304.192.3-304.fi.1.1, 304.192.3-304.fi.1.2, 304.192.3-304.fi.1.3, 304.192.3-304.fi.1.4, 304.192.3-304.fi.1.5, 304.192.3-304.fi.1.6, 304.192.3-304.fi.1.7, 304.192.3-304.fi.1.8, 304.192.3-304.fi.1.9, 304.192.3-304.fi.1.10, 304.192.3-304.fi.1.11, 304.192.3-304.fi.1.12
Cyclic 304-isogeny field degree:	$40$
Cyclic 304-torsion field degree:	$2880$
Full 304-torsion field degree:	$31518720$

Rational points

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

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
16.48.0.j.1	$16$	$2$	$2$	$0$	$0$
152.48.1.cx.1	$152$	$2$	$2$	$1$	$?$
304.48.2.h.1	$304$	$2$	$2$	$2$	$?$

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

Covering curve	Level	Index	Degree	Genus
304.192.5.gp.1	$304$	$2$	$2$	$5$
304.192.5.gp.2	$304$	$2$	$2$	$5$
304.192.5.gr.1	$304$	$2$	$2$	$5$
304.192.5.gr.2	$304$	$2$	$2$	$5$