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: | $\begin{bmatrix}146&123\\141&272\end{bmatrix}$, $\begin{bmatrix}206&63\\251&106\end{bmatrix}$, $\begin{bmatrix}215&22\\264&301\end{bmatrix}$, $\begin{bmatrix}243&46\\2&127\end{bmatrix}$, $\begin{bmatrix}277&242\\90&233\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.96.3.sy.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.iu.1.18 | $24$ | $2$ | $2$ | $1$ | $0$ |
156.96.0-156.c.4.9 | $156$ | $2$ | $2$ | $0$ | $?$ |
312.96.0-156.c.4.27 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.96.1-24.iu.1.15 | $312$ | $2$ | $2$ | $1$ | $?$ |
312.96.2-312.h.2.29 | $312$ | $2$ | $2$ | $2$ | $?$ |
312.96.2-312.h.2.42 | $312$ | $2$ | $2$ | $2$ | $?$ |
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.qp.4.22 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.re.1.16 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.ux.1.13 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.vb.1.16 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.vl.2.4 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.vn.2.9 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.yt.2.3 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.yy.2.9 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.baj.1.14 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bal.2.2 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.baz.1.14 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bbb.3.6 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bcv.4.10 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bcx.4.3 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bdl.4.10 | $312$ | $2$ | $2$ | $5$ |
312.384.5-312.bdn.4.2 | $312$ | $2$ | $2$ | $5$ |