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: | $\begin{bmatrix}30&17\\211&296\end{bmatrix}$, $\begin{bmatrix}108&283\\281&154\end{bmatrix}$, $\begin{bmatrix}116&247\\99&76\end{bmatrix}$, $\begin{bmatrix}238&59\\79&210\end{bmatrix}$, $\begin{bmatrix}303&280\\22&69\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.96.3.td.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 | $24$ | $2$ | $2$ | $1$ | $0$ |
312.96.0-312.ds.1.41 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.96.0-312.ds.1.43 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.96.1-24.ix.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ |
312.96.2-312.h.1.41 | $312$ | $2$ | $2$ | $2$ | $?$ |
312.96.2-312.h.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.qv.1.2 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.rk.3.16 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.vf.1.11 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.vh.4.15 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.xh.4.5 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.xk.4.9 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.yv.4.6 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.yy.3.13 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bas.4.13 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bau.2.9 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bbi.3.15 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bbk.1.9 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bde.1.15 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bdg.4.4 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bdu.2.13 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bdw.4.3 | $312$ | $2$ | $2$ | $5$ |