Invariants
Level: | $120$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $72$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $4 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $12^{6}$ | Cusp orbits | $2\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 6$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 4$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12A4 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}6&59\\17&26\end{bmatrix}$, $\begin{bmatrix}8&61\\109&64\end{bmatrix}$, $\begin{bmatrix}25&44\\8&3\end{bmatrix}$, $\begin{bmatrix}67&38\\2&77\end{bmatrix}$, $\begin{bmatrix}107&70\\118&19\end{bmatrix}$, $\begin{bmatrix}119&102\\114&95\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 120-isogeny field degree: | $96$ |
Cyclic 120-torsion field degree: | $3072$ |
Full 120-torsion field degree: | $491520$ |
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 |
---|---|---|---|---|---|
24.36.1.fy.1 | $24$ | $2$ | $2$ | $1$ | $1$ |
60.36.1.ft.1 | $60$ | $2$ | $2$ | $1$ | $0$ |
120.24.0.gp.1 | $120$ | $3$ | $3$ | $0$ | $?$ |
120.36.2.qv.1 | $120$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.144.7.hyn.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.hyv.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.iaf.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.ian.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.irt.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.isf.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.ith.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.itp.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.jsb.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.jsj.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.jtl.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.jtt.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.kkn.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.kkv.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.kmf.1 | $120$ | $2$ | $2$ | $7$ |
120.144.7.kmn.1 | $120$ | $2$ | $2$ | $7$ |
120.144.9.fbi.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.fbo.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.fia.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.fik.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.lpm.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.lps.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.lya.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.lyk.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.uaq.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.uas.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.ube.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.ubk.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.whc.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.whe.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.wiw.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.wjc.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.zhe.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.zhk.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.zjc.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.zje.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.bbva.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.bbvg.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.bbvs.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.bbvu.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.bedu.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.beee.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.bemm.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.bems.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.bezy.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.bfai.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.bfgu.1 | $120$ | $2$ | $2$ | $9$ |
120.144.9.bfha.1 | $120$ | $2$ | $2$ | $9$ |