Invariants
Level: | $312$ | $\SL_2$-level: | $6$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $6^{4}$ | Cusp orbits | $1^{2}\cdot2$ | ||
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: | 6D1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}29&225\\243&296\end{bmatrix}$, $\begin{bmatrix}73&135\\264&55\end{bmatrix}$, $\begin{bmatrix}209&63\\120&41\end{bmatrix}$, $\begin{bmatrix}279&158\\128&123\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.24.1.ed.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $168$ |
Cyclic 312-torsion field degree: | $16128$ |
Full 312-torsion field degree: | $40255488$ |
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 |
---|---|---|---|---|---|---|
24.24.0-3.a.1.4 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
39.24.0-3.a.1.1 | $39$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
312.16.0-312.c.1.8 | $312$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
312.16.0-312.c.1.11 | $312$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
312.144.1-312.cp.1.13 | $312$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
312.192.5-312.gp.1.2 | $312$ | $4$ | $4$ | $5$ | $?$ | not computed |