Invariants
Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{6}\cdot10^{6}$ | Cusp orbits | $2^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 72$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 10K1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}3&112\\100&11\end{bmatrix}$, $\begin{bmatrix}53&20\\48&1\end{bmatrix}$, $\begin{bmatrix}71&114\\52&29\end{bmatrix}$, $\begin{bmatrix}109&16\\102&65\end{bmatrix}$, $\begin{bmatrix}109&90\\18&67\end{bmatrix}$, $\begin{bmatrix}115&58\\66&83\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.72.1.d.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $16$ |
Cyclic 120-torsion field degree: | $512$ |
Full 120-torsion field degree: | $245760$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
40.72.1-10.a.1.1 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
60.72.1-10.a.1.3 | $60$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
120.288.5-120.dn.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dn.1.19 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.do.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.do.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.do.1.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dq.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dq.1.27 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dq.1.43 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dr.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dr.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dr.1.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dz.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dz.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dz.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ea.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ea.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ea.1.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ec.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ec.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ec.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ed.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ed.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ed.1.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ex.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ex.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ex.1.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ey.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ey.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ey.1.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fa.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fa.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fa.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fb.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fb.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fb.1.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fj.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fj.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fj.1.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fk.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fk.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fk.1.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fm.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fm.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fm.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fn.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fn.1.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fn.1.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.432.13-120.d.1.3 | $120$ | $3$ | $3$ | $13$ | $?$ | not computed |