Invariants
Level: | $184$ | $\SL_2$-level: | $8$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot4\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8I0 |
Level structure
$\GL_2(\Z/184\Z)$-generators: | $\begin{bmatrix}31&156\\176&83\end{bmatrix}$, $\begin{bmatrix}37&20\\170&7\end{bmatrix}$, $\begin{bmatrix}89&154\\40&115\end{bmatrix}$, $\begin{bmatrix}130&45\\9&134\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 184.24.0.bv.2 for the level structure with $-I$) |
Cyclic 184-isogeny field degree: | $24$ |
Cyclic 184-torsion field degree: | $1056$ |
Full 184-torsion field degree: | $8549376$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.24.0-8.n.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
184.24.0-8.n.1.11 | $184$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
184.96.0-184.bb.2.6 | $184$ | $2$ | $2$ | $0$ |
184.96.0-184.bc.1.7 | $184$ | $2$ | $2$ | $0$ |
184.96.0-184.bd.1.8 | $184$ | $2$ | $2$ | $0$ |
184.96.0-184.bf.1.3 | $184$ | $2$ | $2$ | $0$ |
184.96.0-184.bh.1.2 | $184$ | $2$ | $2$ | $0$ |
184.96.0-184.bi.1.2 | $184$ | $2$ | $2$ | $0$ |
184.96.0-184.bk.2.7 | $184$ | $2$ | $2$ | $0$ |
184.96.0-184.bn.1.3 | $184$ | $2$ | $2$ | $0$ |