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: | $\begin{bmatrix}113&18\\132&107\end{bmatrix}$, $\begin{bmatrix}145&8\\114&143\end{bmatrix}$, $\begin{bmatrix}231&22\\122&211\end{bmatrix}$, $\begin{bmatrix}231&212\\170&21\end{bmatrix}$, $\begin{bmatrix}284&139\\89&306\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.96.3.tf.3 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.4.26 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.96.0-156.c.4.27 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.96.1-24.ix.1.12 | $312$ | $2$ | $2$ | $1$ | $?$ |
312.96.2-312.i.1.10 | $312$ | $2$ | $2$ | $2$ | $?$ |
312.96.2-312.i.1.24 | $312$ | $2$ | $2$ | $2$ | $?$ |
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.3.4 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.rs.1.16 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.vg.1.5 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.vi.1.12 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.xi.1.5 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.xm.2.3 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.yw.1.9 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.za.3.11 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.baq.3.3 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.baw.1.11 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bbg.4.5 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bbm.1.15 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bdc.1.9 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bdi.3.12 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bds.1.5 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bdy.3.4 | $312$ | $2$ | $2$ | $5$ |