Invariants
Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24V3 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}11&96\\80&43\end{bmatrix}$, $\begin{bmatrix}33&61\\40&57\end{bmatrix}$, $\begin{bmatrix}39&40\\116&97\end{bmatrix}$, $\begin{bmatrix}79&84\\108&1\end{bmatrix}$, $\begin{bmatrix}81&53\\112&107\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.3.pm.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $12$ |
Cyclic 120-torsion field degree: | $384$ |
Full 120-torsion field degree: | $184320$ |
Rational points
This modular curve has no $\Q_p$ points for $p=23$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.96.1-24.iq.1.8 | $24$ | $2$ | $2$ | $1$ | $0$ |
60.96.1-60.p.1.3 | $60$ | $2$ | $2$ | $1$ | $0$ |
120.48.0-120.dg.1.8 | $120$ | $4$ | $4$ | $0$ | $?$ |
120.96.1-60.p.1.15 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.1-24.iq.1.24 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.1-120.zw.1.37 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.1-120.zw.1.62 | $120$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.384.5-120.bbv.1.8 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bbv.2.15 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bbv.3.2 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bbv.4.3 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bbz.1.7 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bbz.2.13 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bbz.3.4 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bbz.4.6 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bip.1.7 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bip.2.11 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bip.3.4 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bip.4.4 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bit.1.8 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bit.2.14 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bit.3.2 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bit.4.2 | $120$ | $2$ | $2$ | $5$ |