Invariants
Level: | $312$ | $\SL_2$-level: | $8$ | 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: | $4$ (all of which are rational) | Cusp widths | $4^{2}\cdot8^{2}$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8B1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}15&34\\32&197\end{bmatrix}$, $\begin{bmatrix}71&60\\64&245\end{bmatrix}$, $\begin{bmatrix}115&94\\180&253\end{bmatrix}$, $\begin{bmatrix}127&78\\76&185\end{bmatrix}$, $\begin{bmatrix}217&220\\308&289\end{bmatrix}$, $\begin{bmatrix}259&168\\272&205\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.24.1.d.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $112$ |
Cyclic 312-torsion field degree: | $10752$ |
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 |
---|---|---|---|---|---|---|
4.24.0-4.b.1.1 | $4$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
312.24.0-4.b.1.9 | $312$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
312.96.1-312.n.2.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.bb.1.7 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.cy.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.df.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ea.1.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ea.2.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.eb.1.29 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.eb.2.17 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ec.1.21 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ec.2.17 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ed.1.29 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ed.2.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ee.1.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ee.2.9 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ef.1.23 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ef.2.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.eg.1.21 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.eg.2.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.eh.1.23 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.eh.2.9 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ey.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ff.1.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.fo.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.fr.1.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.144.5-312.h.1.70 | $312$ | $3$ | $3$ | $5$ | $?$ | not computed |
312.192.5-312.h.1.53 | $312$ | $4$ | $4$ | $5$ | $?$ | not computed |