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Properties

Label 120.96.5.dn.1
Level $120$
Index $96$
Genus $5$
Cusps $8$
$\Q$-cusps $0$

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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: $8$ (none of which are rational) Cusp widths $4^{2}\cdot8^{2}\cdot12^{2}\cdot24^{2}$ Cusp orbits $2^{4}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $3 \le \gamma \le 8$
$\overline{\Q}$-gonality: $3 \le \gamma \le 5$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 24K5

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}0&119\\109&56\end{bmatrix}$, $\begin{bmatrix}5&6\\18&35\end{bmatrix}$, $\begin{bmatrix}33&2\\14&33\end{bmatrix}$, $\begin{bmatrix}37&68\\4&63\end{bmatrix}$, $\begin{bmatrix}64&65\\103&84\end{bmatrix}$, $\begin{bmatrix}111&2\\98&27\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 120.192.5-120.dn.1.1, 120.192.5-120.dn.1.2, 120.192.5-120.dn.1.3, 120.192.5-120.dn.1.4, 120.192.5-120.dn.1.5, 120.192.5-120.dn.1.6, 120.192.5-120.dn.1.7, 120.192.5-120.dn.1.8, 120.192.5-120.dn.1.9, 120.192.5-120.dn.1.10, 120.192.5-120.dn.1.11, 120.192.5-120.dn.1.12, 120.192.5-120.dn.1.13, 120.192.5-120.dn.1.14, 120.192.5-120.dn.1.15, 120.192.5-120.dn.1.16, 120.192.5-120.dn.1.17, 120.192.5-120.dn.1.18, 120.192.5-120.dn.1.19, 120.192.5-120.dn.1.20, 120.192.5-120.dn.1.21, 120.192.5-120.dn.1.22, 120.192.5-120.dn.1.23, 120.192.5-120.dn.1.24, 120.192.5-120.dn.1.25, 120.192.5-120.dn.1.26, 120.192.5-120.dn.1.27, 120.192.5-120.dn.1.28, 120.192.5-120.dn.1.29, 120.192.5-120.dn.1.30, 120.192.5-120.dn.1.31, 120.192.5-120.dn.1.32
Cyclic 120-isogeny field degree: $24$
Cyclic 120-torsion field degree: $768$
Full 120-torsion field degree: $368640$

Rational points

This modular curve has no real points and no $\Q_p$ points for $p=13$, and therefore no rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
24.48.3.d.1 $24$ $2$ $2$ $3$ $0$
60.48.2.f.1 $60$ $2$ $2$ $2$ $1$
120.24.1.bn.1 $120$ $4$ $4$ $1$ $?$
120.48.2.m.1 $120$ $2$ $2$ $2$ $?$

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

Covering curve Level Index Degree Genus
120.192.9.bf.1 $120$ $2$ $2$ $9$
120.192.9.wh.1 $120$ $2$ $2$ $9$
120.192.9.bcl.1 $120$ $2$ $2$ $9$
120.192.9.bdl.1 $120$ $2$ $2$ $9$
120.192.9.bnh.1 $120$ $2$ $2$ $9$
120.192.9.bnn.1 $120$ $2$ $2$ $9$
120.192.9.bny.1 $120$ $2$ $2$ $9$
120.192.9.boa.1 $120$ $2$ $2$ $9$
120.192.9.bru.1 $120$ $2$ $2$ $9$
120.192.9.brw.1 $120$ $2$ $2$ $9$
120.192.9.bsj.1 $120$ $2$ $2$ $9$
120.192.9.bsp.1 $120$ $2$ $2$ $9$
120.192.9.bvm.1 $120$ $2$ $2$ $9$
120.192.9.bvo.1 $120$ $2$ $2$ $9$
120.192.9.byf.1 $120$ $2$ $2$ $9$
120.192.9.byl.1 $120$ $2$ $2$ $9$
120.288.17.yuq.1 $120$ $3$ $3$ $17$