Invariants
Level: | $24$ | $\SL_2$-level: | $3$ | ||||
Index: | $6$ | $\PSL_2$-index: | $6$ | ||||
Genus: | $0 = 1 + \frac{ 6 }{12} - \frac{ 2 }{4} - \frac{ 0 }{3} - \frac{ 2 }{2}$ | ||||||
Cusps: | $2$ (none of which are rational) | Cusp widths | $3^{2}$ | Cusp orbits | $2$ | ||
Elliptic points: | $2$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 3C0 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.6.0.14 |
Level structure
$\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}3&17\\2&15\end{bmatrix}$, $\begin{bmatrix}7&20\\5&23\end{bmatrix}$, $\begin{bmatrix}9&19\\11&12\end{bmatrix}$, $\begin{bmatrix}21&7\\2&3\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 24-isogeny field degree: | $48$ |
Cyclic 24-torsion field degree: | $384$ |
Full 24-torsion field degree: | $12288$ |
Models
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 252 x^{2} + 24 x y + y^{2} + 2 z^{2} $ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
Cover information
Click on a modular curve in the diagram to see information about it.
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This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
$X_{\mathrm{ns}}^+(3)$ | $3$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
24.12.1.m.1 | $24$ | $2$ | $2$ | $1$ |
24.12.1.o.1 | $24$ | $2$ | $2$ | $1$ |
24.12.1.s.1 | $24$ | $2$ | $2$ | $1$ |
24.12.1.u.1 | $24$ | $2$ | $2$ | $1$ |
24.12.1.bn.1 | $24$ | $2$ | $2$ | $1$ |
24.12.1.bp.1 | $24$ | $2$ | $2$ | $1$ |
24.12.1.bq.1 | $24$ | $2$ | $2$ | $1$ |
24.12.1.bs.1 | $24$ | $2$ | $2$ | $1$ |
24.18.0.c.1 | $24$ | $3$ | $3$ | $0$ |
24.24.1.ew.1 | $24$ | $4$ | $4$ | $1$ |
72.18.0.d.1 | $72$ | $3$ | $3$ | $0$ |
72.54.2.g.1 | $72$ | $9$ | $9$ | $2$ |
120.12.1.cy.1 | $120$ | $2$ | $2$ | $1$ |
120.12.1.da.1 | $120$ | $2$ | $2$ | $1$ |
120.12.1.de.1 | $120$ | $2$ | $2$ | $1$ |
120.12.1.dg.1 | $120$ | $2$ | $2$ | $1$ |
120.12.1.dk.1 | $120$ | $2$ | $2$ | $1$ |
120.12.1.dm.1 | $120$ | $2$ | $2$ | $1$ |
120.12.1.dq.1 | $120$ | $2$ | $2$ | $1$ |
120.12.1.ds.1 | $120$ | $2$ | $2$ | $1$ |
120.30.2.q.1 | $120$ | $5$ | $5$ | $2$ |
120.36.1.lo.1 | $120$ | $6$ | $6$ | $1$ |
120.60.3.ga.1 | $120$ | $10$ | $10$ | $3$ |
168.12.1.cu.1 | $168$ | $2$ | $2$ | $1$ |
168.12.1.cw.1 | $168$ | $2$ | $2$ | $1$ |
168.12.1.da.1 | $168$ | $2$ | $2$ | $1$ |
168.12.1.dc.1 | $168$ | $2$ | $2$ | $1$ |
168.12.1.dg.1 | $168$ | $2$ | $2$ | $1$ |
168.12.1.di.1 | $168$ | $2$ | $2$ | $1$ |
168.12.1.dm.1 | $168$ | $2$ | $2$ | $1$ |
168.12.1.do.1 | $168$ | $2$ | $2$ | $1$ |
168.48.3.gm.1 | $168$ | $8$ | $8$ | $3$ |
168.126.6.e.1 | $168$ | $21$ | $21$ | $6$ |
168.168.9.do.1 | $168$ | $28$ | $28$ | $9$ |
264.12.1.cu.1 | $264$ | $2$ | $2$ | $1$ |
264.12.1.cw.1 | $264$ | $2$ | $2$ | $1$ |
264.12.1.da.1 | $264$ | $2$ | $2$ | $1$ |
264.12.1.dc.1 | $264$ | $2$ | $2$ | $1$ |
264.12.1.dg.1 | $264$ | $2$ | $2$ | $1$ |
264.12.1.di.1 | $264$ | $2$ | $2$ | $1$ |
264.12.1.dm.1 | $264$ | $2$ | $2$ | $1$ |
264.12.1.do.1 | $264$ | $2$ | $2$ | $1$ |
264.72.5.bsu.1 | $264$ | $12$ | $12$ | $5$ |
264.330.20.e.1 | $264$ | $55$ | $55$ | $20$ |
264.330.22.m.1 | $264$ | $55$ | $55$ | $22$ |
312.12.1.cu.1 | $312$ | $2$ | $2$ | $1$ |
312.12.1.cw.1 | $312$ | $2$ | $2$ | $1$ |
312.12.1.da.1 | $312$ | $2$ | $2$ | $1$ |
312.12.1.dc.1 | $312$ | $2$ | $2$ | $1$ |
312.12.1.dg.1 | $312$ | $2$ | $2$ | $1$ |
312.12.1.di.1 | $312$ | $2$ | $2$ | $1$ |
312.12.1.dm.1 | $312$ | $2$ | $2$ | $1$ |
312.12.1.do.1 | $312$ | $2$ | $2$ | $1$ |
312.84.5.u.1 | $312$ | $14$ | $14$ | $5$ |