Invariants
Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $7 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
Cusps: | $20$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot6^{4}\cdot8^{4}\cdot12^{2}\cdot24^{4}$ | Cusp orbits | $2^{10}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 12$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24AK7 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}137&288\\44&155\end{bmatrix}$, $\begin{bmatrix}161&240\\264&19\end{bmatrix}$, $\begin{bmatrix}241&240\\272&35\end{bmatrix}$, $\begin{bmatrix}253&180\\106&235\end{bmatrix}$, $\begin{bmatrix}259&108\\276&97\end{bmatrix}$, $\begin{bmatrix}263&240\\226&223\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.192.7.er.3 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $28$ |
Cyclic 312-torsion field degree: | $2688$ |
Full 312-torsion field degree: | $5031936$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.192.3-24.bq.2.47 | $24$ | $2$ | $2$ | $3$ | $0$ |
312.192.3-24.bq.2.7 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.192.3-312.eq.1.67 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.192.3-312.eq.1.75 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.192.3-312.ex.2.5 | $312$ | $2$ | $2$ | $3$ | $?$ |
312.192.3-312.ex.2.61 | $312$ | $2$ | $2$ | $3$ | $?$ |