Invariants
Level: | $180$ | $\SL_2$-level: | $36$ | Newform level: | $1$ | ||
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 | $2^{9}\cdot18^{3}$ | 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: | 18J1 |
Level structure
$\GL_2(\Z/180\Z)$-generators: | $\begin{bmatrix}16&119\\21&32\end{bmatrix}$, $\begin{bmatrix}24&157\\173&22\end{bmatrix}$, $\begin{bmatrix}94&171\\117&166\end{bmatrix}$, $\begin{bmatrix}115&54\\124&107\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 90.72.1.d.1 for the level structure with $-I$) |
Cyclic 180-isogeny field degree: | $12$ |
Cyclic 180-torsion field degree: | $576$ |
Full 180-torsion field degree: | $1244160$ |
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 |
---|---|---|---|---|---|---|
36.72.0-18.a.1.12 | $36$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
60.48.0-30.a.1.8 | $60$ | $3$ | $3$ | $0$ | $0$ | full Jacobian |
180.72.0-18.a.1.5 | $180$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
180.288.5-180.i.1.2 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.288.5-180.k.1.12 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.288.5-180.u.1.6 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.288.5-180.w.1.4 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.288.5-180.bg.1.2 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.288.5-180.bi.1.5 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.288.5-180.bo.1.9 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.288.5-180.bq.1.1 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.432.7-90.m.1.6 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
180.432.7-90.m.2.3 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
180.432.7-90.o.1.3 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
180.432.10-90.c.1.9 | $180$ | $3$ | $3$ | $10$ | $?$ | not computed |