Invariants
Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24W3 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}12&13\\19&126\end{bmatrix}$, $\begin{bmatrix}31&32\\222&221\end{bmatrix}$, $\begin{bmatrix}159&292\\194&61\end{bmatrix}$, $\begin{bmatrix}230&205\\311&0\end{bmatrix}$, $\begin{bmatrix}242&307\\207&70\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.96.3.tf.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $28$ |
Cyclic 312-torsion field degree: | $1344$ |
Full 312-torsion field degree: | $10063872$ |
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 |
---|---|---|---|---|---|
24.96.1-24.ix.1.22 | $24$ | $2$ | $2$ | $1$ | $0$ |
312.96.0-156.c.1.32 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.96.0-156.c.1.33 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.96.1-24.ix.1.4 | $312$ | $2$ | $2$ | $1$ | $?$ |
312.96.2-312.i.1.41 | $312$ | $2$ | $2$ | $2$ | $?$ |
312.96.2-312.i.1.42 | $312$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
312.384.5-312.qw.1.6 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.rs.2.16 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.vg.1.10 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.vi.2.14 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.xi.3.9 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.xm.4.3 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.yw.2.10 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.za.4.6 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.baq.4.5 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.baw.2.11 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bbg.3.3 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bbm.2.14 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bdc.2.10 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bdi.4.8 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bds.3.9 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bdy.4.6 | $312$ | $2$ | $2$ | $5$ |