Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
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: | 8K1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}5&16\\66&49\end{bmatrix}$, $\begin{bmatrix}49&100\\0&83\end{bmatrix}$, $\begin{bmatrix}71&92\\8&33\end{bmatrix}$, $\begin{bmatrix}71&104\\16&71\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.px.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $24$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $184320$ |
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 |
---|---|---|---|---|---|---|
24.96.0-8.l.1.6 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.96.0-8.l.1.3 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.96.0-120.be.2.9 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.be.2.21 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bg.2.11 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bg.2.21 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.cz.1.6 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.cz.1.21 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-120.dx.2.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.dx.2.23 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.dz.2.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.dz.2.27 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.fq.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.fq.1.10 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
240.384.5-240.ic.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.kj.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.xo.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ya.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bar.2.18 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bas.1.21 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bav.2.18 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.baw.1.17 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bbh.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bbi.1.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bbl.1.21 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bbm.2.27 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bcf.2.22 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bcg.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bcj.1.22 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bck.1.19 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bcv.1.30 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bcw.2.25 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bcz.1.22 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bda.1.21 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bei.1.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.beq.1.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bgl.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bhc.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |