Invariants
Level: | $312$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}107&18\\24&277\end{bmatrix}$, $\begin{bmatrix}173&18\\128&101\end{bmatrix}$, $\begin{bmatrix}233&146\\196&251\end{bmatrix}$, $\begin{bmatrix}255&280\\172&23\end{bmatrix}$, $\begin{bmatrix}307&226\\180&191\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.48.1.dn.2 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $112$ |
Cyclic 312-torsion field degree: | $5376$ |
Full 312-torsion field degree: | $20127744$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
24.48.0-24.i.2.5 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
104.48.1-104.c.1.3 | $104$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.48.0-24.i.2.24 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.0-312.u.1.25 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.0-312.u.1.64 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.1-104.c.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
312.192.1-312.by.1.10 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.cr.1.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.dp.1.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.dr.1.15 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.fy.1.7 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.gc.1.11 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.hf.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.hj.1.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.mh.1.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.ml.1.16 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.nn.1.11 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.nr.1.7 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.op.1.15 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.or.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.ou.1.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.ov.1.10 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.288.9-312.ru.2.57 | $312$ | $3$ | $3$ | $9$ | $?$ | not computed |
312.384.9-312.jk.1.15 | $312$ | $4$ | $4$ | $9$ | $?$ | not computed |