Invariants
Level: | $92$ | $\SL_2$-level: | $4$ | ||||
Index: | $24$ | $\PSL_2$-index: | $12$ | ||||
Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $2^{2}\cdot4^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
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: | 4E0 |
Level structure
$\GL_2(\Z/92\Z)$-generators: | $\begin{bmatrix}27&6\\52&41\end{bmatrix}$, $\begin{bmatrix}35&42\\34&13\end{bmatrix}$, $\begin{bmatrix}41&42\\12&45\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 92.12.0.a.1 for the level structure with $-I$) |
Cyclic 92-isogeny field degree: | $48$ |
Cyclic 92-torsion field degree: | $1056$ |
Full 92-torsion field degree: | $1068672$ |
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 |
---|---|---|---|---|---|
4.12.0-2.a.1.1 | $4$ | $2$ | $2$ | $0$ | $0$ |
92.12.0-2.a.1.1 | $92$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
92.48.0-92.a.1.1 | $92$ | $2$ | $2$ | $0$ |
92.48.0-92.a.1.2 | $92$ | $2$ | $2$ | $0$ |
92.48.0-92.c.1.2 | $92$ | $2$ | $2$ | $0$ |
92.48.0-92.c.1.4 | $92$ | $2$ | $2$ | $0$ |
184.48.0-184.b.1.1 | $184$ | $2$ | $2$ | $0$ |
184.48.0-184.b.1.5 | $184$ | $2$ | $2$ | $0$ |
184.48.0-184.f.1.1 | $184$ | $2$ | $2$ | $0$ |
184.48.0-184.f.1.5 | $184$ | $2$ | $2$ | $0$ |
276.48.0-276.d.1.3 | $276$ | $2$ | $2$ | $0$ |
276.48.0-276.d.1.7 | $276$ | $2$ | $2$ | $0$ |
276.48.0-276.f.1.1 | $276$ | $2$ | $2$ | $0$ |
276.48.0-276.f.1.5 | $276$ | $2$ | $2$ | $0$ |
276.72.2-276.a.1.1 | $276$ | $3$ | $3$ | $2$ |
276.96.1-276.a.1.1 | $276$ | $4$ | $4$ | $1$ |