Properties

Label 120.288.7-120.bmx.1.45
Level $120$
Index $288$
Genus $7$
Cusps $12$
$\Q$-cusps $0$

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Invariants

Level: $120$ $\SL_2$-level: $24$ Newform level: $1$
Index: $288$ $\PSL_2$-index:$144$
Genus: $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$
Cusps: $12$ (none of which are rational) Cusp widths $6^{8}\cdot24^{4}$ Cusp orbits $2^{4}\cdot4$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $3 \le \gamma \le 12$
$\overline{\Q}$-gonality: $3 \le \gamma \le 7$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 24J7

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}33&74\\16&117\end{bmatrix}$, $\begin{bmatrix}41&20\\32&93\end{bmatrix}$, $\begin{bmatrix}47&112\\4&1\end{bmatrix}$, $\begin{bmatrix}79&110\\12&101\end{bmatrix}$, $\begin{bmatrix}101&38\\104&45\end{bmatrix}$, $\begin{bmatrix}105&104\\112&9\end{bmatrix}$
Contains $-I$: no $\quad$ (see 120.144.7.bmx.1 for the level structure with $-I$)
Cyclic 120-isogeny field degree: $24$
Cyclic 120-torsion field degree: $768$
Full 120-torsion field degree: $122880$

Rational points

This modular curve has no $\Q_p$ points for $p=13$, 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
8.48.0-8.i.1.2 $8$ $6$ $6$ $0$ $0$
15.6.0.b.1 $15$ $48$ $24$ $0$ $0$

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
24.144.4-24.ch.1.38 $24$ $2$ $2$ $4$ $0$
60.144.3-60.w.1.11 $60$ $2$ $2$ $3$ $0$
120.144.3-60.w.1.36 $120$ $2$ $2$ $3$ $?$
120.144.3-120.cdt.1.19 $120$ $2$ $2$ $3$ $?$
120.144.3-120.cdt.1.39 $120$ $2$ $2$ $3$ $?$
120.144.3-120.cfk.1.10 $120$ $2$ $2$ $3$ $?$
120.144.3-120.cfk.1.23 $120$ $2$ $2$ $3$ $?$
120.144.4-120.bg.1.9 $120$ $2$ $2$ $4$ $?$
120.144.4-120.bg.1.78 $120$ $2$ $2$ $4$ $?$
120.144.4-24.ch.1.22 $120$ $2$ $2$ $4$ $?$
120.144.4-120.pb.1.14 $120$ $2$ $2$ $4$ $?$
120.144.4-120.pb.1.42 $120$ $2$ $2$ $4$ $?$
120.144.4-120.re.1.7 $120$ $2$ $2$ $4$ $?$
120.144.4-120.re.1.26 $120$ $2$ $2$ $4$ $?$