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: | $8$ (of which $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8F1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}17&12\\270&19\end{bmatrix}$, $\begin{bmatrix}69&56\\74&81\end{bmatrix}$, $\begin{bmatrix}101&140\\144&127\end{bmatrix}$, $\begin{bmatrix}225&280\\122&13\end{bmatrix}$, $\begin{bmatrix}253&256\\276&109\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.48.1.fr.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $56$ |
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 is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
312.48.0-8.i.1.6 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.0-312.e.1.20 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.0-312.e.1.30 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.1-312.d.1.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.48.1-312.d.1.35 | $312$ | $2$ | $2$ | $1$ | $?$ | 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.py.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.py.2.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.pz.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.pz.2.8 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qa.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qa.2.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qb.1.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qb.2.7 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qc.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qc.2.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qd.1.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qd.2.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qe.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qe.2.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qf.1.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qf.2.14 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.288.9-312.bbr.1.46 | $312$ | $3$ | $3$ | $9$ | $?$ | not computed |
312.384.9-312.ov.1.35 | $312$ | $4$ | $4$ | $9$ | $?$ | not computed |