Invariants
Level: | $84$ | $\SL_2$-level: | $28$ | Newform level: | $392$ | ||
Index: | $504$ | $\PSL_2$-index: | $252$ | ||||
Genus: | $16 = 1 + \frac{ 252 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $14^{6}\cdot28^{6}$ | Cusp orbits | $3^{2}\cdot6$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $5 \le \gamma \le 30$ | ||||||
$\overline{\Q}$-gonality: | $5 \le \gamma \le 16$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 28C16 |
Level structure
$\GL_2(\Z/84\Z)$-generators: | $\begin{bmatrix}21&46\\20&63\end{bmatrix}$, $\begin{bmatrix}59&29\\16&35\end{bmatrix}$, $\begin{bmatrix}67&66\\48&65\end{bmatrix}$, $\begin{bmatrix}71&48\\40&67\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 28.252.16.s.1 for the level structure with $-I$) |
Cyclic 84-isogeny field degree: | $32$ |
Cyclic 84-torsion field degree: | $768$ |
Full 84-torsion field degree: | $18432$ |
Rational points
This modular curve has no $\Q_p$ points for $p=11,67$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
84.24.0-28.g.1.2 | $84$ | $21$ | $21$ | $0$ | $?$ |
84.252.7-28.c.1.1 | $84$ | $2$ | $2$ | $7$ | $?$ |
84.252.7-28.c.1.4 | $84$ | $2$ | $2$ | $7$ | $?$ |