Invariants
Level: | $102$ | $\SL_2$-level: | $6$ | Newform level: | $1$ | ||
Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $6^{4}$ | Cusp orbits | $1^{2}\cdot2$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 6D1 |
Level structure
$\GL_2(\Z/102\Z)$-generators: | $\begin{bmatrix}32&57\\99&17\end{bmatrix}$, $\begin{bmatrix}59&51\\30&71\end{bmatrix}$, $\begin{bmatrix}81&35\\20&45\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 102.48.1-102.c.1.1, 102.48.1-102.c.1.2, 204.48.1-102.c.1.1, 204.48.1-102.c.1.2 |
Cyclic 102-isogeny field degree: | $54$ |
Cyclic 102-torsion field degree: | $1728$ |
Full 102-torsion field degree: | $940032$ |
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 |
---|---|---|---|---|---|---|
$X_{\mathrm{sp}}(3)$ | $3$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
102.8.0.b.1 | $102$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
102.12.0.a.1 | $102$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
102.12.1.h.1 | $102$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
102.72.1.c.1 | $102$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
204.96.5.j.1 | $204$ | $4$ | $4$ | $5$ | $?$ | not computed |
306.72.3.d.1 | $306$ | $3$ | $3$ | $3$ | $?$ | not computed |
306.72.3.g.1 | $306$ | $3$ | $3$ | $3$ | $?$ | not computed |
306.72.3.i.1 | $306$ | $3$ | $3$ | $3$ | $?$ | not computed |
306.72.4.b.1 | $306$ | $3$ | $3$ | $4$ | $?$ | not computed |
306.72.5.c.1 | $306$ | $3$ | $3$ | $5$ | $?$ | not computed |