Invariants
Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $3600$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $2^{6}\cdot10^{6}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 10K1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}5&54\\112&83\end{bmatrix}$, $\begin{bmatrix}12&61\\79&90\end{bmatrix}$, $\begin{bmatrix}17&86\\12&103\end{bmatrix}$, $\begin{bmatrix}26&105\\51&62\end{bmatrix}$, $\begin{bmatrix}67&68\\80&39\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 60.72.1.cf.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $16$ |
Cyclic 120-torsion field degree: | $256$ |
Full 120-torsion field degree: | $245760$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | 3600.2.a.be |
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 |
---|---|---|---|---|---|---|
40.72.0-10.a.2.1 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.72.0-10.a.2.9 | $120$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.288.5-60.fq.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.fu.1.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.kp.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.kv.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.pa.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.pg.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.qa.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.qe.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.432.13-60.gn.2.27 | $120$ | $3$ | $3$ | $13$ | $?$ | not computed |
120.288.5-120.bor.1.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bpt.1.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.ddf.1.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dev.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.egs.1.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.eii.1.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.enq.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.eos.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |