Invariants
| Level: | $114$ | $\SL_2$-level: | $6$ | Newform level: | $1$ | ||
| Index: | $18$ | $\PSL_2$-index: | $18$ | ||||
| Genus: | $1 = 1 + \frac{ 18 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 3 }{2}$ | ||||||
| Cusps: | $3$ (of which $1$ is rational) | Cusp widths | $6^{3}$ | Cusp orbits | $1\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $1$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 6C1 |
Level structure
| $\GL_2(\Z/114\Z)$-generators: | $\begin{bmatrix}41&82\\28&7\end{bmatrix}$, $\begin{bmatrix}55&81\\82&83\end{bmatrix}$, $\begin{bmatrix}59&105\\96&59\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 114-isogeny field degree: | $80$ |
| Cyclic 114-torsion field degree: | $2880$ |
| Full 114-torsion field degree: | $1969920$ |
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 |
|---|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(3)$ | $3$ | $6$ | $6$ | $0$ | $0$ | full Jacobian |
| 38.6.0.b.1 | $38$ | $3$ | $3$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 6.9.0.a.1 | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 38.6.0.b.1 | $38$ | $3$ | $3$ | $0$ | $0$ | full Jacobian |
| 114.6.1.a.1 | $114$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 114.36.1.i.1 | $114$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 114.36.1.k.1 | $114$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 114.36.1.m.1 | $114$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 114.36.1.o.1 | $114$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 228.36.1.bg.1 | $228$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 228.36.1.bu.1 | $228$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 228.36.1.ci.1 | $228$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 228.36.1.cw.1 | $228$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 228.36.2.q.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.s.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.bk.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.bm.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.cm.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.cn.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.dc.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.dd.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.du.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.dv.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.ek.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.el.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.fa.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.fc.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.fi.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |
| 228.36.2.fk.1 | $228$ | $2$ | $2$ | $2$ | $?$ | not computed |