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 | $1^{6}\cdot4^{3}\cdot9^{2}\cdot36$ | 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: | 36C1 |
Level structure
$\GL_2(\Z/180\Z)$-generators: | $\begin{bmatrix}28&25\\63&56\end{bmatrix}$, $\begin{bmatrix}79&72\\122&179\end{bmatrix}$, $\begin{bmatrix}144&143\\11&36\end{bmatrix}$, $\begin{bmatrix}165&86\\26&129\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 180.72.1.f.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 |
60.48.0-60.q.1.7 | $60$ | $3$ | $3$ | $0$ | $0$ | full Jacobian |
180.72.0-18.a.1.1 | $180$ | $2$ | $2$ | $0$ | $?$ | 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.b.1.9 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.288.5-180.h.1.3 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.288.5-180.r.1.6 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.288.5-180.t.1.7 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.288.5-180.bl.1.6 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.288.5-180.bn.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.br.1.1 | $180$ | $2$ | $2$ | $5$ | $?$ | not computed |
180.432.7-180.co.1.9 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
180.432.7-180.co.2.10 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
180.432.7-180.cu.1.9 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
180.432.10-180.e.1.10 | $180$ | $3$ | $3$ | $10$ | $?$ | not computed |