Invariants
Level: | $176$ | $\SL_2$-level: | $16$ | ||||
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 | $2^{8}\cdot16^{2}$ | 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: | 16G0 |
Level structure
$\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}9&128\\30&25\end{bmatrix}$, $\begin{bmatrix}45&144\\170&57\end{bmatrix}$, $\begin{bmatrix}93&96\\84&165\end{bmatrix}$, $\begin{bmatrix}119&136\\158&175\end{bmatrix}$, $\begin{bmatrix}133&56\\110&131\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 176.48.0.d.2 for the level structure with $-I$) |
Cyclic 176-isogeny field degree: | $24$ |
Cyclic 176-torsion field degree: | $960$ |
Full 176-torsion field degree: | $3379200$ |
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 |
---|---|---|---|---|---|
16.48.0-8.i.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ |
88.48.0-8.i.1.2 | $88$ | $2$ | $2$ | $0$ | $?$ |
176.48.0-176.e.2.1 | $176$ | $2$ | $2$ | $0$ | $?$ |
176.48.0-176.e.2.32 | $176$ | $2$ | $2$ | $0$ | $?$ |
176.48.0-176.f.1.1 | $176$ | $2$ | $2$ | $0$ | $?$ |
176.48.0-176.f.1.32 | $176$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
176.192.1-176.a.1.2 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.b.2.11 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.c.2.5 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.d.1.3 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.e.2.11 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.f.2.2 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.g.2.2 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.h.2.11 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.i.1.4 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.j.2.5 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.k.2.11 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.l.1.2 | $176$ | $2$ | $2$ | $1$ |
176.192.3-176.bm.2.5 | $176$ | $2$ | $2$ | $3$ |
176.192.3-176.bo.2.3 | $176$ | $2$ | $2$ | $3$ |
176.192.3-176.bt.2.3 | $176$ | $2$ | $2$ | $3$ |
176.192.3-176.bw.2.3 | $176$ | $2$ | $2$ | $3$ |