Invariants
Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $12^{4}\cdot24^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 9$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 9$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24C9 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}83&130\\40&309\end{bmatrix}$, $\begin{bmatrix}103&38\\272&201\end{bmatrix}$, $\begin{bmatrix}119&170\\248&25\end{bmatrix}$, $\begin{bmatrix}141&268\\88&97\end{bmatrix}$, $\begin{bmatrix}305&298\\40&265\end{bmatrix}$, $\begin{bmatrix}309&124\\200&141\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.144.9.bbr.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $56$ |
Cyclic 312-torsion field degree: | $5376$ |
Full 312-torsion field degree: | $6709248$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.144.4-24.ch.1.38 | $24$ | $2$ | $2$ | $4$ | $0$ |
312.96.1-312.fr.1.5 | $312$ | $3$ | $3$ | $1$ | $?$ |
312.144.4-312.l.1.40 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-312.l.1.64 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.4-24.ch.1.15 | $312$ | $2$ | $2$ | $4$ | $?$ |
312.144.5-312.h.1.7 | $312$ | $2$ | $2$ | $5$ | $?$ |
312.144.5-312.h.1.70 | $312$ | $2$ | $2$ | $5$ | $?$ |