Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | 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 | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{4}\cdot4$ | ||
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: | 8F1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}29&80\\42&17\end{bmatrix}$, $\begin{bmatrix}53&104\\0&77\end{bmatrix}$, $\begin{bmatrix}77&64\\66&109\end{bmatrix}$, $\begin{bmatrix}107&32\\110&87\end{bmatrix}$, $\begin{bmatrix}109&104\\83&71\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.ix.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $24$ |
Cyclic 120-torsion field degree: | $768$ |
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 |
---|---|---|---|---|---|---|
24.48.0-8.q.1.6 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.48.0-8.q.1.4 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.48.0-60.h.1.2 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-60.h.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.1-120.m.1.10 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.48.1-120.m.1.13 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.192.1-120.qo.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qo.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qo.2.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qo.2.16 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qp.1.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qp.1.10 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qp.2.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qp.2.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.288.9-120.cje.1.21 | $120$ | $3$ | $3$ | $9$ | $?$ | not computed |
120.384.9-120.ws.1.8 | $120$ | $4$ | $4$ | $9$ | $?$ | not computed |
120.480.17-120.no.1.11 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |
240.192.3-240.qk.1.8 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.qk.1.21 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.qo.1.16 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.qo.1.17 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.qs.1.6 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.qs.1.22 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.qw.1.14 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.qw.1.18 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sa.1.11 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sa.1.21 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sf.1.11 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sf.1.21 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.si.1.11 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.si.1.21 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sj.1.13 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sj.1.19 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sr.1.12 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sr.1.19 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sz.1.10 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sz.1.20 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.td.1.10 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.td.1.20 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.tg.1.12 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.tg.1.19 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |