Invariants
Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $1^{4}\cdot2^{2}\cdot3^{4}\cdot6^{2}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24J1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}33&10\\14&281\end{bmatrix}$, $\begin{bmatrix}34&247\\209&120\end{bmatrix}$, $\begin{bmatrix}40&111\\171&304\end{bmatrix}$, $\begin{bmatrix}212&219\\55&268\end{bmatrix}$, $\begin{bmatrix}283&184\\78&185\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.96.1.tg.4 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $28$ |
Cyclic 312-torsion field degree: | $1344$ |
Full 312-torsion field degree: | $10063872$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
24.96.1-24.ix.1.22 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
312.96.0-156.c.3.31 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-156.c.3.47 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.dq.2.6 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.dq.2.28 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.1-24.ix.1.25 | $312$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
312.384.5-312.qw.4.2 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.rk.2.16 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.vg.2.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.vh.2.15 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.xi.3.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.xk.4.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.yw.1.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.yy.4.10 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bhm.2.13 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bho.4.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bic.2.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bie.4.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bjy.4.12 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bka.1.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bko.4.11 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bkq.3.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |