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: | $\begin{bmatrix}12&37\\277&156\end{bmatrix}$, $\begin{bmatrix}15&10\\94&159\end{bmatrix}$, $\begin{bmatrix}260&249\\287&202\end{bmatrix}$, $\begin{bmatrix}261&196\\52&237\end{bmatrix}$, $\begin{bmatrix}283&236\\150&233\end{bmatrix}$, $\begin{bmatrix}292&185\\213&296\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 312.48.1.baa.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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 3.8.0-3.a.1.1 | $3$ | $12$ | $12$ | $0$ | $0$ | full Jacobian |
| 104.12.0.ba.1 | $104$ | $8$ | $4$ | $0$ | $?$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 12.48.0-12.g.1.10 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 312.48.0-12.g.1.17 | $312$ | $2$ | $2$ | $0$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 312.192.1-312.rn.1.31 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.rn.2.17 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.rn.3.23 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.rn.4.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.rp.1.29 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.rp.2.21 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.rp.3.21 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.rp.4.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.sx.1.29 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.sx.2.21 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.sx.3.21 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.sx.4.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.sz.1.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.sz.2.23 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.sz.3.17 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.1-312.sz.4.7 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 312.192.3-312.gd.1.62 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.hq.1.31 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.ky.1.40 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.la.1.31 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.mc.1.29 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.me.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.mo.1.29 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.mq.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.nz.1.47 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.oa.1.32 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.pe.1.27 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.ph.1.32 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.pv.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.pw.1.32 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.qg.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.qj.1.32 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.su.1.8 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.su.2.10 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.su.3.16 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.su.4.26 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.sw.1.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.sw.2.12 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.sw.3.12 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.sw.4.28 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.ts.1.4 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.ts.2.12 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.ts.3.12 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.ts.4.28 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.tu.1.2 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.tu.2.16 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.tu.3.10 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.192.3-312.tu.4.32 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
| 312.288.5-312.po.1.2 | $312$ | $3$ | $3$ | $5$ | $?$ | not computed |