Properties

Label 120.240.7-120.cu.1.38
Level $120$
Index $240$
Genus $7$
Cusps $8$
$\Q$-cusps $0$

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Invariants

Level: $120$ $\SL_2$-level: $40$ Newform level: $1$
Index: $240$ $\PSL_2$-index:$120$
Genus: $7 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$
Cusps: $8$ (none of which are rational) Cusp widths $5^{4}\cdot10^{2}\cdot40^{2}$ Cusp orbits $2^{2}\cdot4$
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: 40G7

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}5&106\\26&5\end{bmatrix}$, $\begin{bmatrix}25&8\\12&113\end{bmatrix}$, $\begin{bmatrix}48&59\\77&82\end{bmatrix}$, $\begin{bmatrix}49&78\\22&17\end{bmatrix}$, $\begin{bmatrix}73&20\\38&27\end{bmatrix}$, $\begin{bmatrix}101&118\\72&19\end{bmatrix}$
Contains $-I$: no $\quad$ (see 120.120.7.cu.1 for the level structure with $-I$)
Cyclic 120-isogeny field degree: $48$
Cyclic 120-torsion field degree: $1536$
Full 120-torsion field degree: $147456$

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
$X_{\mathrm{ns}}^+(5)$ $5$ $24$ $12$ $0$ $0$
24.24.0-24.y.1.9 $24$ $10$ $10$ $0$ $0$

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
24.24.0-24.y.1.9 $24$ $10$ $10$ $0$ $0$
40.120.3-20.c.1.5 $40$ $2$ $2$ $3$ $0$
120.120.3-20.c.1.19 $120$ $2$ $2$ $3$ $?$

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

Covering curve Level Index Degree Genus
120.480.13-120.bvk.1.14 $120$ $2$ $2$ $13$
120.480.13-120.bvm.1.6 $120$ $2$ $2$ $13$
120.480.13-120.bvo.1.10 $120$ $2$ $2$ $13$
120.480.13-120.bvq.1.2 $120$ $2$ $2$ $13$
120.480.13-120.bwy.1.6 $120$ $2$ $2$ $13$
120.480.13-120.bxa.1.16 $120$ $2$ $2$ $13$
120.480.13-120.bxc.1.4 $120$ $2$ $2$ $13$
120.480.13-120.bxe.1.12 $120$ $2$ $2$ $13$
120.480.13-120.bzc.1.12 $120$ $2$ $2$ $13$
120.480.13-120.bze.1.4 $120$ $2$ $2$ $13$
120.480.13-120.bzg.1.16 $120$ $2$ $2$ $13$
120.480.13-120.bzi.1.8 $120$ $2$ $2$ $13$
120.480.13-120.caq.1.16 $120$ $2$ $2$ $13$
120.480.13-120.cas.1.20 $120$ $2$ $2$ $13$
120.480.13-120.cau.1.32 $120$ $2$ $2$ $13$
120.480.13-120.caw.1.24 $120$ $2$ $2$ $13$
120.480.15-120.es.1.6 $120$ $2$ $2$ $15$
120.480.15-120.eu.1.20 $120$ $2$ $2$ $15$
120.480.15-120.ft.1.20 $120$ $2$ $2$ $15$
120.480.15-120.fv.1.20 $120$ $2$ $2$ $15$
120.480.15-120.hy.1.18 $120$ $2$ $2$ $15$
120.480.15-120.ib.1.2 $120$ $2$ $2$ $15$
120.480.15-120.jb.1.22 $120$ $2$ $2$ $15$
120.480.15-120.jc.1.6 $120$ $2$ $2$ $15$
120.480.15-120.km.1.20 $120$ $2$ $2$ $15$
120.480.15-120.ko.1.4 $120$ $2$ $2$ $15$
120.480.15-120.kq.1.28 $120$ $2$ $2$ $15$
120.480.15-120.ks.1.8 $120$ $2$ $2$ $15$
120.480.15-120.ma.1.24 $120$ $2$ $2$ $15$
120.480.15-120.mc.1.8 $120$ $2$ $2$ $15$
120.480.15-120.me.1.20 $120$ $2$ $2$ $15$
120.480.15-120.mg.1.4 $120$ $2$ $2$ $15$
120.480.15-120.ou.1.12 $120$ $2$ $2$ $15$
120.480.15-120.ow.1.8 $120$ $2$ $2$ $15$
120.480.15-120.oy.1.16 $120$ $2$ $2$ $15$
120.480.15-120.pa.1.8 $120$ $2$ $2$ $15$
120.480.15-120.qy.1.26 $120$ $2$ $2$ $15$
120.480.15-120.ra.1.6 $120$ $2$ $2$ $15$
120.480.15-120.rc.1.30 $120$ $2$ $2$ $15$
120.480.15-120.re.1.14 $120$ $2$ $2$ $15$
120.480.15-120.sm.1.11 $120$ $2$ $2$ $15$
120.480.15-120.so.1.6 $120$ $2$ $2$ $15$
120.480.15-120.sq.1.10 $120$ $2$ $2$ $15$
120.480.15-120.ss.1.6 $120$ $2$ $2$ $15$
120.480.15-120.uq.1.32 $120$ $2$ $2$ $15$
120.480.15-120.us.1.16 $120$ $2$ $2$ $15$
120.480.15-120.uu.1.23 $120$ $2$ $2$ $15$
120.480.15-120.uw.1.6 $120$ $2$ $2$ $15$