Invariants
Level: | $330$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-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 | $2^{2}\cdot10^{2}$ | 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: | 10D1 |
Level structure
$\GL_2(\Z/330\Z)$-generators: | $\begin{bmatrix}136&153\\313&56\end{bmatrix}$, $\begin{bmatrix}221&174\\75&137\end{bmatrix}$, $\begin{bmatrix}275&119\\214&255\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 110.24.1.d.2 for the level structure with $-I$) |
Cyclic 330-isogeny field degree: | $144$ |
Cyclic 330-torsion field degree: | $11520$ |
Full 330-torsion field degree: | $38016000$ |
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 |
---|---|---|---|---|---|---|
30.24.0-5.a.2.2 | $30$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
165.24.0-5.a.2.1 | $165$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
330.144.1-110.d.2.1 | $330$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
330.240.5-110.f.1.4 | $330$ | $5$ | $5$ | $5$ | $?$ | not computed |
330.144.5-330.bm.1.9 | $330$ | $3$ | $3$ | $5$ | $?$ | not computed |
330.192.5-330.m.1.12 | $330$ | $4$ | $4$ | $5$ | $?$ | not computed |