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Properties

Label 304.192.5.bo.1
Level $304$
Index $192$
Genus $5$
Cusps $24$
$\Q$-cusps $4$

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Invariants

Level: $304$ $\SL_2$-level: $16$ Newform level: $1$
Index: $192$ $\PSL_2$-index:$192$
Genus: $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$
Cusps: $24$ (of which $4$ are rational) Cusp widths $4^{8}\cdot8^{12}\cdot16^{4}$ Cusp orbits $1^{4}\cdot4^{5}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2 \le \gamma \le 5$
$\overline{\Q}$-gonality: $2 \le \gamma \le 5$
Rational cusps: $4$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 16O5

Level structure

$\GL_2(\Z/304\Z)$-generators: $\begin{bmatrix}23&72\\204&243\end{bmatrix}$, $\begin{bmatrix}31&76\\192&113\end{bmatrix}$, $\begin{bmatrix}63&132\\232&245\end{bmatrix}$, $\begin{bmatrix}89&136\\92&85\end{bmatrix}$, $\begin{bmatrix}255&80\\52&191\end{bmatrix}$, $\begin{bmatrix}257&196\\240&19\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 304.384.5-304.bo.1.1, 304.384.5-304.bo.1.2, 304.384.5-304.bo.1.3, 304.384.5-304.bo.1.4, 304.384.5-304.bo.1.5, 304.384.5-304.bo.1.6, 304.384.5-304.bo.1.7, 304.384.5-304.bo.1.8, 304.384.5-304.bo.1.9, 304.384.5-304.bo.1.10, 304.384.5-304.bo.1.11, 304.384.5-304.bo.1.12, 304.384.5-304.bo.1.13, 304.384.5-304.bo.1.14, 304.384.5-304.bo.1.15, 304.384.5-304.bo.1.16, 304.384.5-304.bo.1.17, 304.384.5-304.bo.1.18, 304.384.5-304.bo.1.19, 304.384.5-304.bo.1.20, 304.384.5-304.bo.1.21, 304.384.5-304.bo.1.22, 304.384.5-304.bo.1.23, 304.384.5-304.bo.1.24
Cyclic 304-isogeny field degree: $40$
Cyclic 304-torsion field degree: $5760$
Full 304-torsion field degree: $15759360$

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
8.96.1.g.1 $8$ $2$ $2$ $1$ $0$
304.96.2.a.1 $304$ $2$ $2$ $2$ $?$
304.96.2.d.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
304.384.13.d.2 $304$ $2$ $2$ $13$
304.384.13.r.1 $304$ $2$ $2$ $13$
304.384.13.bk.1 $304$ $2$ $2$ $13$
304.384.13.bz.1 $304$ $2$ $2$ $13$
304.384.13.de.1 $304$ $2$ $2$ $13$
304.384.13.dg.2 $304$ $2$ $2$ $13$
304.384.13.di.1 $304$ $2$ $2$ $13$
304.384.13.dj.1 $304$ $2$ $2$ $13$
304.384.13.dr.2 $304$ $2$ $2$ $13$
304.384.13.ee.1 $304$ $2$ $2$ $13$
304.384.13.ff.2 $304$ $2$ $2$ $13$
304.384.13.ft.2 $304$ $2$ $2$ $13$
304.384.17.du.4 $304$ $2$ $2$ $17$
304.384.17.dv.2 $304$ $2$ $2$ $17$
304.384.17.dx.3 $304$ $2$ $2$ $17$
304.384.17.dz.3 $304$ $2$ $2$ $17$