Invariants
Level: | $252$ | $\SL_2$-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
$\GL_2(\Z/252\Z)$-generators: | $\begin{bmatrix}74&113\\67&210\end{bmatrix}$, $\begin{bmatrix}98&207\\73&154\end{bmatrix}$, $\begin{bmatrix}145&222\\176&143\end{bmatrix}$, $\begin{bmatrix}216&85\\41&188\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 252.72.1.k.1 for the level structure with $-I$) |
Cyclic 252-isogeny field degree: | $16$ |
Cyclic 252-torsion field degree: | $1152$ |
Full 252-torsion field degree: | $5225472$ |
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 |
84.48.0-84.r.1.7 | $84$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
252.72.0-18.a.1.4 | $252$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
252.288.5-252.d.1.10 | $252$ | $2$ | $2$ | $5$ | $?$ | not computed |
252.288.5-252.g.1.8 | $252$ | $2$ | $2$ | $5$ | $?$ | not computed |
252.288.5-252.y.1.2 | $252$ | $2$ | $2$ | $5$ | $?$ | not computed |
252.288.5-252.bb.1.4 | $252$ | $2$ | $2$ | $5$ | $?$ | not computed |
252.288.5-252.bg.1.6 | $252$ | $2$ | $2$ | $5$ | $?$ | not computed |
252.288.5-252.bj.1.5 | $252$ | $2$ | $2$ | $5$ | $?$ | not computed |
252.288.5-252.bs.1.2 | $252$ | $2$ | $2$ | $5$ | $?$ | not computed |
252.288.5-252.bv.1.1 | $252$ | $2$ | $2$ | $5$ | $?$ | not computed |
252.432.7-252.ff.1.12 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.ff.2.11 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.fo.1.3 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.fo.2.5 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.fx.1.3 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.fx.2.7 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.ga.1.3 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.ga.2.3 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.gd.1.11 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.10-252.bu.1.12 | $252$ | $3$ | $3$ | $10$ | $?$ | not computed |