Invariants
Level: | $252$ | $\SL_2$-level: | $36$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $4 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $6^{3}\cdot18^{3}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 4$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 18D4 |
Level structure
$\GL_2(\Z/252\Z)$-generators: | $\begin{bmatrix}38&189\\35&82\end{bmatrix}$, $\begin{bmatrix}44&205\\239&84\end{bmatrix}$, $\begin{bmatrix}107&238\\182&201\end{bmatrix}$, $\begin{bmatrix}186&239\\77&228\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 252.72.4.v.1 for the level structure with $-I$) |
Cyclic 252-isogeny field degree: | $48$ |
Cyclic 252-torsion field degree: | $3456$ |
Full 252-torsion field degree: | $5225472$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
36.72.2-18.c.1.3 | $36$ | $2$ | $2$ | $2$ | $0$ |
84.48.0-84.p.1.2 | $84$ | $3$ | $3$ | $0$ | $?$ |
252.72.2-18.c.1.5 | $252$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
252.288.9-252.v.1.2 | $252$ | $2$ | $2$ | $9$ |
252.288.9-252.x.1.4 | $252$ | $2$ | $2$ | $9$ |
252.288.9-252.gy.1.1 | $252$ | $2$ | $2$ | $9$ |
252.288.9-252.hb.1.1 | $252$ | $2$ | $2$ | $9$ |
252.288.9-252.hl.1.4 | $252$ | $2$ | $2$ | $9$ |
252.288.9-252.ho.1.8 | $252$ | $2$ | $2$ | $9$ |
252.288.9-252.hu.1.3 | $252$ | $2$ | $2$ | $9$ |
252.288.9-252.hw.1.10 | $252$ | $2$ | $2$ | $9$ |
252.432.10-252.bw.1.10 | $252$ | $3$ | $3$ | $10$ |
252.432.10-252.cj.1.4 | $252$ | $3$ | $3$ | $10$ |
252.432.10-252.cj.2.12 | $252$ | $3$ | $3$ | $10$ |
252.432.10-252.cs.1.8 | $252$ | $3$ | $3$ | $10$ |
252.432.10-252.cs.2.14 | $252$ | $3$ | $3$ | $10$ |
252.432.10-252.db.1.8 | $252$ | $3$ | $3$ | $10$ |
252.432.10-252.db.2.14 | $252$ | $3$ | $3$ | $10$ |
252.432.10-252.de.1.8 | $252$ | $3$ | $3$ | $10$ |
252.432.10-252.de.2.8 | $252$ | $3$ | $3$ | $10$ |
252.432.10-252.dh.1.8 | $252$ | $3$ | $3$ | $10$ |