Invariants
Level: | $152$ | $\SL_2$-level: | $8$ | ||||
Index: | $48$ | $\PSL_2$-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 | $2^{2}\cdot4^{3}\cdot8$ | 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: | 8J0 |
Level structure
$\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}13&132\\62&115\end{bmatrix}$, $\begin{bmatrix}63&72\\18&39\end{bmatrix}$, $\begin{bmatrix}83&16\\122&143\end{bmatrix}$, $\begin{bmatrix}107&104\\98&53\end{bmatrix}$, $\begin{bmatrix}111&112\\76&77\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 8.24.0.d.1 for the level structure with $-I$) |
Cyclic 152-isogeny field degree: | $40$ |
Cyclic 152-torsion field degree: | $2880$ |
Full 152-torsion field degree: | $3939840$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points, including 136 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map of degree 24 to the modular curve $X(1)$ :
$\displaystyle j$ | $=$ | $\displaystyle 2^2\,\frac{x^{24}(256x^{8}+256x^{6}y^{2}+80x^{4}y^{4}+8x^{2}y^{6}+y^{8})^{3}}{y^{8}x^{28}(2x^{2}+y^{2})^{2}(4x^{2}+y^{2})^{4}}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
76.24.0-4.b.1.3 | $76$ | $2$ | $2$ | $0$ | $?$ |
152.24.0-4.b.1.8 | $152$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
152.96.0-8.a.1.10 | $152$ | $2$ | $2$ | $0$ |
152.96.0-8.b.2.6 | $152$ | $2$ | $2$ | $0$ |
152.96.0-8.d.1.2 | $152$ | $2$ | $2$ | $0$ |
152.96.0-8.e.1.5 | $152$ | $2$ | $2$ | $0$ |
152.96.0-8.g.1.3 | $152$ | $2$ | $2$ | $0$ |
152.96.0-152.g.2.8 | $152$ | $2$ | $2$ | $0$ |
152.96.0-8.h.1.5 | $152$ | $2$ | $2$ | $0$ |
152.96.0-152.h.2.6 | $152$ | $2$ | $2$ | $0$ |
152.96.0-8.j.1.5 | $152$ | $2$ | $2$ | $0$ |
152.96.0-8.k.2.3 | $152$ | $2$ | $2$ | $0$ |
152.96.0-152.k.1.3 | $152$ | $2$ | $2$ | $0$ |
152.96.0-152.l.1.3 | $152$ | $2$ | $2$ | $0$ |
152.96.0-152.o.1.4 | $152$ | $2$ | $2$ | $0$ |
152.96.0-152.p.2.4 | $152$ | $2$ | $2$ | $0$ |
152.96.0-152.s.2.1 | $152$ | $2$ | $2$ | $0$ |
152.96.0-152.t.1.1 | $152$ | $2$ | $2$ | $0$ |
152.96.1-8.e.2.1 | $152$ | $2$ | $2$ | $1$ |
152.96.1-8.i.1.1 | $152$ | $2$ | $2$ | $1$ |
152.96.1-8.l.1.1 | $152$ | $2$ | $2$ | $1$ |
152.96.1-8.m.2.1 | $152$ | $2$ | $2$ | $1$ |
152.96.1-152.bc.2.12 | $152$ | $2$ | $2$ | $1$ |
152.96.1-152.bd.2.10 | $152$ | $2$ | $2$ | $1$ |
152.96.1-152.bg.2.5 | $152$ | $2$ | $2$ | $1$ |
152.96.1-152.bh.1.5 | $152$ | $2$ | $2$ | $1$ |