Invariants
| Level: | $252$ | $\SL_2$-level: | $14$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $2^{3}\cdot14^{3}$ | Cusp orbits | $3^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 14D2 |
Level structure
| $\GL_2(\Z/252\Z)$-generators: | $\begin{bmatrix}63&104\\29&23\end{bmatrix}$, $\begin{bmatrix}190&33\\143&55\end{bmatrix}$, $\begin{bmatrix}222&151\\181&63\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 252.48.2.t.2 for the level structure with $-I$) |
| Cyclic 252-isogeny field degree: | $72$ |
| Cyclic 252-torsion field degree: | $5184$ |
| Full 252-torsion field degree: | $7838208$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 63.48.0-63.b.1.2 | $63$ | $2$ | $2$ | $0$ | $0$ |
| 84.32.0-84.d.1.7 | $84$ | $3$ | $3$ | $0$ | $?$ |
| 252.48.0-63.b.1.6 | $252$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 252.288.4-252.bb.2.11 | $252$ | $3$ | $3$ | $4$ |
| 252.288.10-252.ek.1.9 | $252$ | $3$ | $3$ | $10$ |
| 252.384.11-252.ba.1.8 | $252$ | $4$ | $4$ | $11$ |
| 252.384.11-252.bt.2.7 | $252$ | $4$ | $4$ | $11$ |