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Properties

Label 120.96.5.wt.1
Level $120$
Index $96$
Genus $5$
Cusps $8$
$\Q$-cusps $4$

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Invariants

Level: $120$ $\SL_2$-level: $24$ Newform level: $1$
Index: $96$ $\PSL_2$-index:$96$
Genus: $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$
Cusps: $8$ (of which $4$ are rational) Cusp widths $4^{2}\cdot8^{2}\cdot12^{2}\cdot24^{2}$ Cusp orbits $1^{4}\cdot2^{2}$
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: 24J5

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}9&118\\10&21\end{bmatrix}$, $\begin{bmatrix}48&59\\17&12\end{bmatrix}$, $\begin{bmatrix}56&19\\15&52\end{bmatrix}$, $\begin{bmatrix}76&29\\3&44\end{bmatrix}$, $\begin{bmatrix}76&81\\7&44\end{bmatrix}$, $\begin{bmatrix}118&29\\99&74\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 120.192.5-120.wt.1.1, 120.192.5-120.wt.1.2, 120.192.5-120.wt.1.3, 120.192.5-120.wt.1.4, 120.192.5-120.wt.1.5, 120.192.5-120.wt.1.6, 120.192.5-120.wt.1.7, 120.192.5-120.wt.1.8, 120.192.5-120.wt.1.9, 120.192.5-120.wt.1.10, 120.192.5-120.wt.1.11, 120.192.5-120.wt.1.12, 120.192.5-120.wt.1.13, 120.192.5-120.wt.1.14, 120.192.5-120.wt.1.15, 120.192.5-120.wt.1.16, 120.192.5-120.wt.1.17, 120.192.5-120.wt.1.18, 120.192.5-120.wt.1.19, 120.192.5-120.wt.1.20, 120.192.5-120.wt.1.21, 120.192.5-120.wt.1.22, 120.192.5-120.wt.1.23, 120.192.5-120.wt.1.24, 120.192.5-120.wt.1.25, 120.192.5-120.wt.1.26, 120.192.5-120.wt.1.27, 120.192.5-120.wt.1.28, 120.192.5-120.wt.1.29, 120.192.5-120.wt.1.30, 120.192.5-120.wt.1.31, 120.192.5-120.wt.1.32
Cyclic 120-isogeny field degree: $12$
Cyclic 120-torsion field degree: $384$
Full 120-torsion field degree: $368640$

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
24.48.2.i.1 $24$ $2$ $2$ $2$ $0$
60.48.2.f.1 $60$ $2$ $2$ $2$ $1$
120.24.0.jd.1 $120$ $4$ $4$ $0$ $?$
120.48.3.da.1 $120$ $2$ $2$ $3$ $?$

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

Covering curve Level Index Degree Genus
120.192.9.oq.1 $120$ $2$ $2$ $9$
120.192.9.ul.1 $120$ $2$ $2$ $9$
120.192.9.ws.1 $120$ $2$ $2$ $9$
120.192.9.wz.1 $120$ $2$ $2$ $9$
120.192.9.but.1 $120$ $2$ $2$ $9$
120.192.9.bux.1 $120$ $2$ $2$ $9$
120.192.9.bvi.1 $120$ $2$ $2$ $9$
120.192.9.bvm.1 $120$ $2$ $2$ $9$
120.192.9.cdq.1 $120$ $2$ $2$ $9$
120.192.9.cdu.1 $120$ $2$ $2$ $9$
120.192.9.cef.1 $120$ $2$ $2$ $9$
120.192.9.cej.1 $120$ $2$ $2$ $9$
120.192.9.cio.1 $120$ $2$ $2$ $9$
120.192.9.cis.1 $120$ $2$ $2$ $9$
120.192.9.cjd.1 $120$ $2$ $2$ $9$
120.192.9.cjh.1 $120$ $2$ $2$ $9$
120.288.17.btwu.1 $120$ $3$ $3$ $17$