Invariants
Level: | $312$ | $\SL_2$-level: | $24$ | 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 $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot3^{2}\cdot6\cdot8\cdot24$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
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: | 24G1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}96&299\\311&60\end{bmatrix}$, $\begin{bmatrix}112&77\\21&284\end{bmatrix}$, $\begin{bmatrix}115&230\\244&225\end{bmatrix}$, $\begin{bmatrix}197&48\\194&91\end{bmatrix}$, $\begin{bmatrix}243&34\\164&229\end{bmatrix}$, $\begin{bmatrix}273&118\\148&255\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.48.1.zv.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $28$ |
Cyclic 312-torsion field degree: | $2688$ |
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 |
---|---|---|---|---|---|---|
24.48.0-12.g.1.14 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
156.48.0-12.g.1.3 | $156$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.24.0-104.z.1.11 | $312$ | $4$ | $4$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
312.192.1-312.rc.1.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.rc.2.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.rc.3.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.rc.4.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.re.1.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.re.2.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.re.3.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.re.4.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.sm.1.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.sm.2.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.sm.3.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.sm.4.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.so.1.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.so.2.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.so.3.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.so.4.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.3-312.gd.1.49 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ht.1.26 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.jh.1.12 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ji.1.26 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.lv.1.3 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.lx.1.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.mh.1.11 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.mj.1.1 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.od.1.36 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.oe.1.21 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ow.1.28 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.oz.1.21 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.pr.1.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ps.1.9 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.py.1.12 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.qb.1.9 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.sj.1.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.sj.2.6 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.sj.3.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.sj.4.6 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.sl.1.6 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.sl.2.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.sl.3.6 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.sl.4.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.th.1.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.th.2.6 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.th.3.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.th.4.6 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.tj.1.6 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.tj.2.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.tj.3.6 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.tj.4.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.288.5-312.pd.1.38 | $312$ | $3$ | $3$ | $5$ | $?$ | not computed |