Invariants
Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot3^{2}\cdot6\cdot8\cdot24$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24G1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}43&114\\76&65\end{bmatrix}$, $\begin{bmatrix}48&65\\119&54\end{bmatrix}$, $\begin{bmatrix}68&85\\17&48\end{bmatrix}$, $\begin{bmatrix}69&86\\74&105\end{bmatrix}$, $\begin{bmatrix}104&103\\29&54\end{bmatrix}$, $\begin{bmatrix}114&37\\109&66\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.zu.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $12$ |
Cyclic 120-torsion field degree: | $384$ |
Full 120-torsion field degree: | $368640$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.48.0-12.g.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.24.0-40.y.1.10 | $120$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
120.48.0-12.g.1.14 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
120.192.1-120.rb.1.26 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rb.2.25 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rb.3.27 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rb.4.25 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rd.1.20 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rd.2.18 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rd.3.22 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rd.4.18 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sl.1.26 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sl.2.25 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sl.3.27 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sl.4.25 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sn.1.20 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sn.2.18 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sn.3.22 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sn.4.18 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.3-120.gc.1.66 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.hq.1.5 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.jg.1.31 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ji.1.21 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.lu.1.20 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.lw.1.6 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.mg.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.mi.1.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.oc.1.29 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.of.1.21 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ox.1.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.oy.1.5 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pq.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pt.1.9 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pz.1.19 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qa.1.5 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.si.1.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.si.2.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.si.3.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.si.4.26 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sk.1.13 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sk.2.13 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sk.3.27 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sk.4.29 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tg.1.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tg.2.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tg.3.20 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tg.4.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ti.1.13 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ti.2.13 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ti.3.26 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ti.4.27 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.288.5-120.bee.1.19 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.480.17-120.bre.1.25 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |