Properties

Label 120.480.15-120.hs.1.32
Level $120$
Index $480$
Genus $15$
Cusps $12$
$\Q$-cusps $0$

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Invariants

Level: $120$ $\SL_2$-level: $40$ Newform level: $1$
Index: $480$ $\PSL_2$-index:$240$
Genus: $15 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$
Cusps: $12$ (none of which are rational) Cusp widths $10^{8}\cdot40^{4}$ Cusp orbits $4^{3}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $4 \le \gamma \le 28$
$\overline{\Q}$-gonality: $4 \le \gamma \le 15$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 40C15

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}1&93\\64&109\end{bmatrix}$, $\begin{bmatrix}39&17\\76&1\end{bmatrix}$, $\begin{bmatrix}77&110\\80&27\end{bmatrix}$, $\begin{bmatrix}85&99\\24&23\end{bmatrix}$, $\begin{bmatrix}87&82\\92&1\end{bmatrix}$
Contains $-I$: no $\quad$ (see 120.240.15.hs.1 for the level structure with $-I$)
Cyclic 120-isogeny field degree: $48$
Cyclic 120-torsion field degree: $768$
Full 120-torsion field degree: $73728$

Rational points

This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known 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
$X_{\mathrm{ns}}^+(5)$ $5$ $48$ $24$ $0$ $0$
24.48.0-24.be.1.8 $24$ $10$ $10$ $0$ $0$

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
24.48.0-24.be.1.8 $24$ $10$ $10$ $0$ $0$
40.240.7-40.bu.1.16 $40$ $2$ $2$ $7$ $4$
120.240.7-40.bu.1.4 $120$ $2$ $2$ $7$ $?$
120.240.7-120.di.1.17 $120$ $2$ $2$ $7$ $?$
120.240.7-120.di.1.60 $120$ $2$ $2$ $7$ $?$
120.240.7-120.dj.1.13 $120$ $2$ $2$ $7$ $?$
120.240.7-120.dj.1.64 $120$ $2$ $2$ $7$ $?$