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Properties

Label 120.192.9.bjm.1
Level $120$
Index $192$
Genus $9$
Cusps $16$
$\Q$-cusps $0$

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Invariants

Level: $120$ $\SL_2$-level: $24$ Newform level: $1$
Index: $192$ $\PSL_2$-index:$192$
Genus: $9 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$
Cusps: $16$ (none of which are rational) Cusp widths $4^{4}\cdot8^{4}\cdot12^{4}\cdot24^{4}$ Cusp orbits $2^{8}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $3 \le \gamma \le 16$
$\overline{\Q}$-gonality: $3 \le \gamma \le 9$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 24AF9

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}89&116\\96&25\end{bmatrix}$, $\begin{bmatrix}93&113\\68&51\end{bmatrix}$, $\begin{bmatrix}105&113\\112&103\end{bmatrix}$, $\begin{bmatrix}109&16\\48&101\end{bmatrix}$, $\begin{bmatrix}111&23\\100&1\end{bmatrix}$, $\begin{bmatrix}119&11\\40&93\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 120.384.9-120.bjm.1.1, 120.384.9-120.bjm.1.2, 120.384.9-120.bjm.1.3, 120.384.9-120.bjm.1.4, 120.384.9-120.bjm.1.5, 120.384.9-120.bjm.1.6, 120.384.9-120.bjm.1.7, 120.384.9-120.bjm.1.8, 120.384.9-120.bjm.1.9, 120.384.9-120.bjm.1.10, 120.384.9-120.bjm.1.11, 120.384.9-120.bjm.1.12, 120.384.9-120.bjm.1.13, 120.384.9-120.bjm.1.14, 120.384.9-120.bjm.1.15, 120.384.9-120.bjm.1.16, 120.384.9-120.bjm.1.17, 120.384.9-120.bjm.1.18, 120.384.9-120.bjm.1.19, 120.384.9-120.bjm.1.20, 120.384.9-120.bjm.1.21, 120.384.9-120.bjm.1.22, 120.384.9-120.bjm.1.23, 120.384.9-120.bjm.1.24, 240.384.9-120.bjm.1.1, 240.384.9-120.bjm.1.2, 240.384.9-120.bjm.1.3, 240.384.9-120.bjm.1.4, 240.384.9-120.bjm.1.5, 240.384.9-120.bjm.1.6, 240.384.9-120.bjm.1.7, 240.384.9-120.bjm.1.8, 240.384.9-120.bjm.1.9, 240.384.9-120.bjm.1.10, 240.384.9-120.bjm.1.11, 240.384.9-120.bjm.1.12, 240.384.9-120.bjm.1.13, 240.384.9-120.bjm.1.14, 240.384.9-120.bjm.1.15, 240.384.9-120.bjm.1.16
Cyclic 120-isogeny field degree: $12$
Cyclic 120-torsion field degree: $384$
Full 120-torsion field degree: $184320$

Rational points

This modular curve has no $\Q_p$ points for $p=23$, and therefore no 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
$X_0(3)$ $3$ $48$ $48$ $0$ $0$
40.48.1.ea.1 $40$ $4$ $4$ $1$ $0$

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
12.96.3.m.1 $12$ $2$ $2$ $3$ $0$
40.48.1.ea.1 $40$ $4$ $4$ $1$ $0$
120.96.3.kz.1 $120$ $2$ $2$ $3$ $?$
120.96.5.bh.1 $120$ $2$ $2$ $5$ $?$
120.96.5.qs.1 $120$ $2$ $2$ $5$ $?$
120.96.5.qt.1 $120$ $2$ $2$ $5$ $?$
120.96.5.baw.1 $120$ $2$ $2$ $5$ $?$
120.96.5.bax.1 $120$ $2$ $2$ $5$ $?$

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

Covering curve Level Index Degree Genus
120.384.17.fdm.1 $120$ $2$ $2$ $17$
120.384.17.fdm.2 $120$ $2$ $2$ $17$
120.384.17.fdn.1 $120$ $2$ $2$ $17$
120.384.17.fdn.2 $120$ $2$ $2$ $17$
120.384.17.fdo.1 $120$ $2$ $2$ $17$
120.384.17.fdo.2 $120$ $2$ $2$ $17$
120.384.17.fdp.1 $120$ $2$ $2$ $17$
120.384.17.fdp.2 $120$ $2$ $2$ $17$
240.384.21.dau.1 $240$ $2$ $2$ $21$
240.384.21.dbo.1 $240$ $2$ $2$ $21$
240.384.21.dce.1 $240$ $2$ $2$ $21$
240.384.21.dcq.1 $240$ $2$ $2$ $21$
240.384.21.dug.1 $240$ $2$ $2$ $21$
240.384.21.dug.2 $240$ $2$ $2$ $21$
240.384.21.duo.1 $240$ $2$ $2$ $21$
240.384.21.duo.2 $240$ $2$ $2$ $21$
240.384.21.dxe.1 $240$ $2$ $2$ $21$
240.384.21.dxe.2 $240$ $2$ $2$ $21$
240.384.21.dxm.1 $240$ $2$ $2$ $21$
240.384.21.dxm.2 $240$ $2$ $2$ $21$
240.384.21.een.1 $240$ $2$ $2$ $21$
240.384.21.eez.1 $240$ $2$ $2$ $21$
240.384.21.efp.1 $240$ $2$ $2$ $21$
240.384.21.egj.1 $240$ $2$ $2$ $21$