Invariants
Level: | $60$ | $\SL_2$-level: | $10$ | Newform level: | $400$ | ||
Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (none of which are rational) | Cusp widths | $2^{2}\cdot10^{2}$ | Cusp orbits | $2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | $0$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 10D1 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.24.1.99 |
Level structure
$\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}26&45\\1&44\end{bmatrix}$, $\begin{bmatrix}37&30\\5&53\end{bmatrix}$, $\begin{bmatrix}51&5\\40&3\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 60-isogeny field degree: | $24$ |
Cyclic 60-torsion field degree: | $384$ |
Full 60-torsion field degree: | $92160$ |
Jacobian
Conductor: | $2^{4}\cdot5^{2}$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | 400.2.a.c |
Models
Embedded model Embedded model in $\mathbb{P}^{3}$
$ 0 $ | $=$ | $ 3 x^{2} - y^{2} + y z + 2 y w $ |
$=$ | $12 x^{2} + 33 y^{2} - 2 y z - 4 y w + 4 z^{2} + z w + w^{2}$ |
Singular plane model Singular plane model
$ 0 $ | $=$ | $ 4 x^{4} + 15 x^{2} y z - 6 x^{2} z^{2} + 15 y^{2} z^{2} - 45 y z^{3} + 315 z^{4} $ |
Rational points
This modular curve has no real points, and therefore no rational points.
Maps between models of this curve
Birational map from embedded model to plane model:
$\displaystyle X$ | $=$ | $\displaystyle x$ |
$\displaystyle Y$ | $=$ | $\displaystyle w$ |
$\displaystyle Z$ | $=$ | $\displaystyle \frac{1}{3}y$ |
Maps to other modular curves
$j$-invariant map of degree 24 from the embedded model of this modular curve to the modular curve $X(1)$ :
$\displaystyle j$ | $=$ | $\displaystyle 3^3\,\frac{55575716yz^{5}+1092428840yz^{4}w+2930693600yz^{3}w^{2}+1910000320yz^{2}w^{3}-65693120yzw^{4}-26277248yw^{5}+90233679z^{6}+289341588z^{5}w-171366300z^{4}w^{2}-917829280z^{3}w^{3}-449948400z^{2}w^{4}+10759488zw^{5}+3586496w^{6}}{7184yz^{5}+1454900yz^{4}w+4116305yz^{3}w^{2}+2059900yz^{2}w^{3}-1026455yzw^{4}-410582yw^{5}-259744z^{6}-739848z^{5}w-684420z^{4}w^{2}+166895z^{3}w^{3}+223545z^{2}w^{4}+168117zw^{5}+56039w^{6}}$ |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
15.12.0.b.2 | $15$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
20.12.1.b.1 | $20$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
60.12.0.bo.2 | $60$ | $2$ | $2$ | $0$ | $0$ | 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 |
---|---|---|---|---|---|---|
60.72.1.by.2 | $60$ | $3$ | $3$ | $1$ | $0$ | dimension zero |
60.72.5.co.2 | $60$ | $3$ | $3$ | $5$ | $0$ | $1^{2}\cdot2$ |
60.96.5.bs.1 | $60$ | $4$ | $4$ | $5$ | $0$ | $1^{2}\cdot2$ |
60.96.5.ce.2 | $60$ | $4$ | $4$ | $5$ | $0$ | $1^{2}\cdot2$ |
60.120.5.cp.1 | $60$ | $5$ | $5$ | $5$ | $0$ | $1^{2}\cdot2$ |
300.120.5.k.1 | $300$ | $5$ | $5$ | $5$ | $?$ | not computed |