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: | $4$ (of which $2$ are rational) | Cusp widths | $4^{2}\cdot8^{2}$ | 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: | 8B1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}15&136\\100&155\end{bmatrix}$, $\begin{bmatrix}55&185\\48&65\end{bmatrix}$, $\begin{bmatrix}123&46\\224&163\end{bmatrix}$, $\begin{bmatrix}183&83\\112&305\end{bmatrix}$, $\begin{bmatrix}209&93\\84&91\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 104.24.1.n.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 |
---|---|---|---|---|---|---|
12.24.0-4.d.1.2 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
312.24.0-4.d.1.2 | $312$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
312.96.1-104.cv.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-104.cy.1.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-104.dg.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-104.dn.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-104.dz.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-104.ea.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-104.en.1.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-104.eo.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ji.1.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.jm.1.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.lc.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ln.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.ml.1.2 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.mq.1.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.oc.1.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.96.1-312.og.1.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.144.5-312.bx.1.12 | $312$ | $3$ | $3$ | $5$ | $?$ | not computed |
312.192.5-312.bh.1.7 | $312$ | $4$ | $4$ | $5$ | $?$ | not computed |