Invariants
Level: | $184$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8O0 |
Level structure
$\GL_2(\Z/184\Z)$-generators: | $\begin{bmatrix}49&0\\140&109\end{bmatrix}$, $\begin{bmatrix}121&136\\138&167\end{bmatrix}$, $\begin{bmatrix}129&168\\20&19\end{bmatrix}$, $\begin{bmatrix}165&72\\62&3\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 184.48.0.bb.1 for the level structure with $-I$) |
Cyclic 184-isogeny field degree: | $24$ |
Cyclic 184-torsion field degree: | $2112$ |
Full 184-torsion field degree: | $4274688$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
184.48.0-8.i.1.12 | $184$ | $2$ | $2$ | $0$ | $?$ |
184.48.0-184.i.1.1 | $184$ | $2$ | $2$ | $0$ | $?$ |
184.48.0-184.i.1.13 | $184$ | $2$ | $2$ | $0$ | $?$ |
184.48.0-184.bv.1.7 | $184$ | $2$ | $2$ | $0$ | $?$ |
184.48.0-184.bv.1.10 | $184$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
184.192.1-184.q.1.2 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.br.1.1 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.cc.1.2 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.cg.1.1 | $184$ | $2$ | $2$ | $1$ |