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: | $\begin{bmatrix}5&26\\300&271\end{bmatrix}$, $\begin{bmatrix}21&76\\118&267\end{bmatrix}$, $\begin{bmatrix}162&281\\107&60\end{bmatrix}$, $\begin{bmatrix}185&270\\208&19\end{bmatrix}$, $\begin{bmatrix}217&300\\188&185\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.96.1.tg.2 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.2.7 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-156.c.2.23 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.dq.2.37 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.0-312.dq.2.38 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.96.1-24.ix.1.17 | $312$ | $2$ | $2$ | $1$ | $?$ | 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.2.12 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.rk.1.16 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.vg.2.6 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.vh.1.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.xi.1.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.xk.2.9 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.yw.2.10 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.yy.3.13 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bhm.1.13 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bho.3.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bic.1.15 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bie.3.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bjy.3.14 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bka.2.10 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bko.3.10 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.384.5-312.bkq.1.5 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |