Invariants
| Level: | $102$ | $\SL_2$-level: | $6$ | ||||
| Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{3}\cdot6^{3}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 6I0 |
Level structure
| $\GL_2(\Z/102\Z)$-generators: | $\begin{bmatrix}6&1\\13&96\end{bmatrix}$, $\begin{bmatrix}29&66\\92&79\end{bmatrix}$, $\begin{bmatrix}68&61\\63&4\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 102.48.0-102.b.1.1, 102.48.0-102.b.1.2, 102.48.0-102.b.1.3, 102.48.0-102.b.1.4, 204.48.0-102.b.1.1, 204.48.0-102.b.1.2, 204.48.0-102.b.1.3, 204.48.0-102.b.1.4, 204.48.0-102.b.1.5, 204.48.0-102.b.1.6, 204.48.0-102.b.1.7, 204.48.0-102.b.1.8, 204.48.0-102.b.1.9, 204.48.0-102.b.1.10, 204.48.0-102.b.1.11, 204.48.0-102.b.1.12 |
| Cyclic 102-isogeny field degree: | $18$ |
| Cyclic 102-torsion field degree: | $576$ |
| Full 102-torsion field degree: | $940032$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_0(6)$ | $6$ | $2$ | $2$ | $0$ | $0$ |
| 102.6.0.a.1 | $102$ | $4$ | $4$ | $0$ | $?$ |
| 102.8.0.b.1 | $102$ | $3$ | $3$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 102.72.1.c.1 | $102$ | $3$ | $3$ | $1$ |
| 204.48.1.m.1 | $204$ | $2$ | $2$ | $1$ |
| 204.48.1.o.1 | $204$ | $2$ | $2$ | $1$ |
| 204.48.1.bd.1 | $204$ | $2$ | $2$ | $1$ |
| 204.48.1.be.1 | $204$ | $2$ | $2$ | $1$ |
| 204.48.1.bl.1 | $204$ | $2$ | $2$ | $1$ |
| 204.48.1.bm.1 | $204$ | $2$ | $2$ | $1$ |
| 204.48.1.bs.1 | $204$ | $2$ | $2$ | $1$ |
| 204.48.1.bu.1 | $204$ | $2$ | $2$ | $1$ |
| 306.72.1.c.1 | $306$ | $3$ | $3$ | $1$ |
| 306.72.4.g.1 | $306$ | $3$ | $3$ | $4$ |
| 306.72.4.j.1 | $306$ | $3$ | $3$ | $4$ |