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 $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}33&76\\88&55\end{bmatrix}$, $\begin{bmatrix}39&86\\80&111\end{bmatrix}$, $\begin{bmatrix}41&68\\56&99\end{bmatrix}$, $\begin{bmatrix}55&58\\24&7\end{bmatrix}$, $\begin{bmatrix}81&8\\92&43\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.ef.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
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 |
---|---|---|---|---|---|---|
8.48.0-8.e.2.13 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.48.0-8.e.2.5 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-120.t.2.31 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-120.t.2.47 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.1-120.d.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.48.1-120.d.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ | 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.ba.2.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.cy.2.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ep.2.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ex.2.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ii.2.5 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.iq.2.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.kf.2.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.kn.2.13 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.me.2.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.mm.2.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ob.2.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.oj.2.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.pg.2.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.po.2.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qb.2.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qf.2.15 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.288.9-120.tv.1.40 | $120$ | $3$ | $3$ | $9$ | $?$ | not computed |
120.384.9-120.kp.1.58 | $120$ | $4$ | $4$ | $9$ | $?$ | not computed |
120.480.17-120.gj.1.27 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |