Invariants
Level: | $312$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $3^{8}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
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: | 12S1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}61&140\\48&311\end{bmatrix}$, $\begin{bmatrix}139&150\\114&85\end{bmatrix}$, $\begin{bmatrix}199&36\\144&115\end{bmatrix}$, $\begin{bmatrix}217&236\\87&89\end{bmatrix}$, $\begin{bmatrix}241&230\\36&35\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.72.1.ca.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $56$ |
Cyclic 312-torsion field degree: | $2688$ |
Full 312-torsion field degree: | $13418496$ |
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 |
---|---|---|---|---|---|---|
6.72.0-6.a.1.1 | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
312.48.0-312.ft.1.2 | $312$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
312.48.0-312.ft.1.32 | $312$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
312.72.0-6.a.1.4 | $312$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
312.288.5-312.m.1.2 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.dl.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.ho.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.hr.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.bbr.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.bbs.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.bby.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.bbz.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.btf.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.btg.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.btw.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.bua.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.bzk.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.bzn.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.caf.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |
312.288.5-312.cai.1.1 | $312$ | $2$ | $2$ | $5$ | $?$ | not computed |