Properties

Label 120.96.0-120.bm.2.10
Level $120$
Index $96$
Genus $0$
Cusps $10$
$\Q$-cusps $2$

Related objects

Downloads

Learn more

Invariants

Level: $120$ $\SL_2$-level: $8$
Index: $96$ $\PSL_2$-index:$48$
Genus: $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$
Cusps: $10$ (of which $2$ are rational) Cusp widths $4^{8}\cdot8^{2}$ Cusp orbits $1^{2}\cdot2^{2}\cdot4$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
$\Q$-gonality: $1$
$\overline{\Q}$-gonality: $1$
Rational cusps: $2$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 8N0

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}33&76\\88&57\end{bmatrix}$, $\begin{bmatrix}47&56\\70&11\end{bmatrix}$, $\begin{bmatrix}57&76\\106&91\end{bmatrix}$, $\begin{bmatrix}113&92\\86&45\end{bmatrix}$, $\begin{bmatrix}119&16\\26&17\end{bmatrix}$
Contains $-I$: no $\quad$ (see 120.48.0.bm.2 for the level structure with $-I$)
Cyclic 120-isogeny field degree: $48$
Cyclic 120-torsion field degree: $1536$
Full 120-torsion field degree: $368640$

Models

This modular curve is isomorphic to $\mathbb{P}^1$.

Rational points

This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
24.48.0-8.e.1.2 $24$ $2$ $2$ $0$ $0$
40.48.0-8.e.1.5 $40$ $2$ $2$ $0$ $0$
120.48.0-120.e.1.12 $120$ $2$ $2$ $0$ $?$
120.48.0-120.e.1.32 $120$ $2$ $2$ $0$ $?$
120.48.0-120.t.1.22 $120$ $2$ $2$ $0$ $?$
120.48.0-120.t.1.52 $120$ $2$ $2$ $0$ $?$

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

Covering curve Level Index Degree Genus
120.192.1-120.bf.1.10 $120$ $2$ $2$ $1$
120.192.1-120.db.1.6 $120$ $2$ $2$ $1$
120.192.1-120.eo.1.8 $120$ $2$ $2$ $1$
120.192.1-120.ew.1.12 $120$ $2$ $2$ $1$
120.192.1-120.ij.1.2 $120$ $2$ $2$ $1$
120.192.1-120.ir.1.12 $120$ $2$ $2$ $1$
120.192.1-120.ke.1.16 $120$ $2$ $2$ $1$
120.192.1-120.km.1.4 $120$ $2$ $2$ $1$
120.192.1-120.mf.1.2 $120$ $2$ $2$ $1$
120.192.1-120.mn.1.12 $120$ $2$ $2$ $1$
120.192.1-120.oa.1.16 $120$ $2$ $2$ $1$
120.192.1-120.oi.1.4 $120$ $2$ $2$ $1$
120.192.1-120.ph.1.10 $120$ $2$ $2$ $1$
120.192.1-120.pp.1.6 $120$ $2$ $2$ $1$
120.192.1-120.qb.1.8 $120$ $2$ $2$ $1$
120.192.1-120.qf.1.12 $120$ $2$ $2$ $1$
120.288.8-120.ed.2.48 $120$ $3$ $3$ $8$
120.384.7-120.dr.1.17 $120$ $4$ $4$ $7$
120.480.16-120.cb.2.15 $120$ $5$ $5$ $16$