Invariants
| Level: | $120$ | $\SL_2$-level: | $12$ | Newform level: | $144$ | ||
| 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 | $6^{12}$ | 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: | 6F1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}17&96\\30&17\end{bmatrix}$, $\begin{bmatrix}18&5\\113&102\end{bmatrix}$, $\begin{bmatrix}34&93\\93&64\end{bmatrix}$, $\begin{bmatrix}84&107\\11&84\end{bmatrix}$, $\begin{bmatrix}90&49\\49&54\end{bmatrix}$, $\begin{bmatrix}113&18\\48&77\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 12.72.1.b.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $245760$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 144.2.a.a |
Models
Weierstrass model Weierstrass model
| $ y^{2} $ | $=$ | $ x^{3} - 1 $ |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Maps to other modular curves
$j$-invariant map of degree 72 from the Weierstrass model of this modular curve to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle -\frac{(y^{2}-3z^{2})^{3}(y^{6}-225y^{4}z^{2}-405y^{2}z^{4}-243z^{6})^{3}}{z^{2}y^{6}(y^{2}+z^{2})^{2}(y^{2}+9z^{2})^{6}}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 120.48.0-12.d.1.8 | $120$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
| 120.48.0-12.d.1.11 | $120$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
| 120.72.0-6.a.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.72.0-6.a.1.8 | $120$ | $2$ | $2$ | $0$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 120.288.3-12.b.1.5 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.288.3-12.b.1.7 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.288.3-24.b.1.9 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.288.3-24.b.1.15 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.288.3-60.d.1.6 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.288.3-60.d.1.12 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.288.3-120.d.1.11 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.288.3-120.d.1.23 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 120.288.5-12.i.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-12.k.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-12.l.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-12.n.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-60.ca.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-60.cc.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-24.cf.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-60.cg.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-60.ci.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-24.cs.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-24.cz.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-24.dn.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.oa.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.oo.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.pq.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.qe.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.7-12.bb.1.5 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.288.7-12.bb.1.7 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.288.7-60.fl.1.8 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.288.7-60.fl.1.10 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.288.7-24.or.1.9 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.288.7-24.or.1.15 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.288.7-120.cbg.1.6 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |
| 120.288.7-120.cbg.1.26 | $120$ | $2$ | $2$ | $7$ | $?$ | not computed |