Invariants
| Level: | $110$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
| Index: | $72$ | $\PSL_2$-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 | $2^{6}\cdot10^{6}$ | 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: | 10K1 |
Level structure
| $\GL_2(\Z/110\Z)$-generators: | $\begin{bmatrix}2&23\\7&56\end{bmatrix}$, $\begin{bmatrix}26&65\\67&18\end{bmatrix}$, $\begin{bmatrix}90&1\\97&46\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 110.144.1-110.c.1.1, 110.144.1-110.c.1.2, 110.144.1-110.c.1.3, 110.144.1-110.c.1.4, 220.144.1-110.c.1.1, 220.144.1-110.c.1.2, 220.144.1-110.c.1.3, 220.144.1-110.c.1.4, 220.144.1-110.c.1.5, 220.144.1-110.c.1.6, 220.144.1-110.c.1.7, 220.144.1-110.c.1.8, 220.144.1-110.c.1.9, 220.144.1-110.c.1.10, 220.144.1-110.c.1.11, 220.144.1-110.c.1.12, 330.144.1-110.c.1.1, 330.144.1-110.c.1.2, 330.144.1-110.c.1.3, 330.144.1-110.c.1.4 |
| Cyclic 110-isogeny field degree: | $12$ |
| Cyclic 110-torsion field degree: | $240$ |
| Full 110-torsion field degree: | $528000$ |
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 |
|---|---|---|---|---|---|---|
| $X_{\pm1}(5)$ | $5$ | $6$ | $6$ | $0$ | $0$ | full Jacobian |
| 22.6.0.a.1 | $22$ | $12$ | $12$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_{\pm1}(10)$ | $10$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 110.24.1.c.1 | $110$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
| 110.36.0.b.1 | $110$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 110.36.1.a.1 | $110$ | $2$ | $2$ | $1$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 110.360.13.c.1 | $110$ | $5$ | $5$ | $13$ | $?$ | not computed |
| 220.144.5.ce.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 220.144.5.ci.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 220.144.5.ea.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 220.144.5.ee.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 220.144.5.ge.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 220.144.5.gi.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 220.144.5.gu.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 220.144.5.gy.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 330.216.13.bg.2 | $330$ | $3$ | $3$ | $13$ | $?$ | not computed |
| 330.288.13.i.2 | $330$ | $4$ | $4$ | $13$ | $?$ | not computed |