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: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8O0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}5&8\\107&9\end{bmatrix}$, $\begin{bmatrix}7&80\\62&117\end{bmatrix}$, $\begin{bmatrix}17&32\\119&3\end{bmatrix}$, $\begin{bmatrix}103&0\\47&37\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.0.el.1 for the level structure with $-I$) |
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 therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.48.0-8.ba.1.7 | $24$ | $2$ | $2$ | $0$ | $0$ |
40.48.0-8.ba.1.8 | $40$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-120.dh.1.8 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.dh.1.15 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.ej.1.7 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.ej.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.288.8-120.tg.2.8 | $120$ | $3$ | $3$ | $8$ |
120.384.7-120.mv.2.2 | $120$ | $4$ | $4$ | $7$ |
120.480.16-120.gg.2.2 | $120$ | $5$ | $5$ | $16$ |
240.192.1-240.kb.1.14 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.kh.2.13 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.kr.2.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.kx.1.10 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.uj.1.7 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ul.2.9 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ur.2.1 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ut.1.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ban.2.11 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bap.1.14 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bav.1.16 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bax.2.14 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bdv.2.5 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.beb.1.7 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.bel.1.8 | $240$ | $2$ | $2$ | $1$ |
240.192.1-240.ber.2.11 | $240$ | $2$ | $2$ | $1$ |