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: | $10$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
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: | 8N0 |
Level structure
$\GL_2(\Z/184\Z)$-generators: | $\begin{bmatrix}33&12\\96&105\end{bmatrix}$, $\begin{bmatrix}55&106\\64&161\end{bmatrix}$, $\begin{bmatrix}135&180\\136&123\end{bmatrix}$, $\begin{bmatrix}157&60\\32&33\end{bmatrix}$, $\begin{bmatrix}179&126\\20&69\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 184.48.0.b.2 for the level structure with $-I$) |
Cyclic 184-isogeny field degree: | $48$ |
Cyclic 184-torsion field degree: | $2112$ |
Full 184-torsion field degree: | $4274688$ |
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 |
---|---|---|---|---|---|
8.48.0-4.b.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
184.48.0-4.b.1.6 | $184$ | $2$ | $2$ | $0$ | $?$ |
184.48.0-184.h.1.12 | $184$ | $2$ | $2$ | $0$ | $?$ |
184.48.0-184.h.1.21 | $184$ | $2$ | $2$ | $0$ | $?$ |
184.48.0-184.i.2.8 | $184$ | $2$ | $2$ | $0$ | $?$ |
184.48.0-184.i.2.25 | $184$ | $2$ | $2$ | $0$ | $?$ |
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.a.1.2 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.b.2.1 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.e.2.1 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.f.1.2 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.l.1.14 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.m.2.8 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.n.1.13 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.o.2.15 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.p.1.1 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.q.2.2 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.w.2.2 | $184$ | $2$ | $2$ | $1$ |
184.192.1-184.x.1.1 | $184$ | $2$ | $2$ | $1$ |
184.192.3-184.j.2.7 | $184$ | $2$ | $2$ | $3$ |
184.192.3-184.k.2.7 | $184$ | $2$ | $2$ | $3$ |
184.192.3-184.m.2.7 | $184$ | $2$ | $2$ | $3$ |
184.192.3-184.p.1.7 | $184$ | $2$ | $2$ | $3$ |