Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | ||||
Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 4 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (none of which are rational) | Cusp widths | $4^{2}\cdot8^{2}$ | Cusp orbits | $2^{2}$ | ||
Elliptic points: | $4$ 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: | 8H0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}10&77\\119&2\end{bmatrix}$, $\begin{bmatrix}77&110\\114&89\end{bmatrix}$, $\begin{bmatrix}86&67\\111&46\end{bmatrix}$, $\begin{bmatrix}90&61\\79&94\end{bmatrix}$, $\begin{bmatrix}103&98\\118&39\end{bmatrix}$ |
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: | $1474560$ |
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 |
---|---|---|---|---|---|
24.12.0.bv.1 | $24$ | $2$ | $2$ | $0$ | $0$ |
40.12.0.cb.1 | $40$ | $2$ | $2$ | $0$ | $0$ |
60.12.0.bn.1 | $60$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.48.1.er.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.ii.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.og.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.op.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.sv.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.th.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.tk.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.tw.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.blz.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.bmj.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.bqi.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.bqo.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.btl.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.btt.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.buq.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.buy.1 | $120$ | $2$ | $2$ | $1$ |
120.72.2.wr.1 | $120$ | $3$ | $3$ | $2$ |
120.96.5.bbf.1 | $120$ | $4$ | $4$ | $5$ |
120.120.8.qr.1 | $120$ | $5$ | $5$ | $8$ |
120.144.7.lqd.1 | $120$ | $6$ | $6$ | $7$ |
120.240.15.deh.1 | $120$ | $10$ | $10$ | $15$ |