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Properties

Label 152.24.0.bf.1
Level $152$
Index $24$
Genus $0$
Cusps $6$
$\Q$-cusps $2$

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Invariants

Level: $152$ $\SL_2$-level: $8$
Index: $24$ $\PSL_2$-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 $2^{4}\cdot8^{2}$ 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: 8G0

Level structure

$\GL_2(\Z/152\Z)$-generators: $\begin{bmatrix}11&104\\14&31\end{bmatrix}$, $\begin{bmatrix}19&104\\45&69\end{bmatrix}$, $\begin{bmatrix}85&104\\18&119\end{bmatrix}$, $\begin{bmatrix}99&16\\39&107\end{bmatrix}$, $\begin{bmatrix}131&72\\21&17\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 152.48.0-152.bf.1.1, 152.48.0-152.bf.1.2, 152.48.0-152.bf.1.3, 152.48.0-152.bf.1.4, 152.48.0-152.bf.1.5, 152.48.0-152.bf.1.6, 152.48.0-152.bf.1.7, 152.48.0-152.bf.1.8, 152.48.0-152.bf.1.9, 152.48.0-152.bf.1.10, 152.48.0-152.bf.1.11, 152.48.0-152.bf.1.12, 304.48.0-152.bf.1.1, 304.48.0-152.bf.1.2, 304.48.0-152.bf.1.3, 304.48.0-152.bf.1.4, 304.48.0-152.bf.1.5, 304.48.0-152.bf.1.6, 304.48.0-152.bf.1.7, 304.48.0-152.bf.1.8
Cyclic 152-isogeny field degree: $20$
Cyclic 152-torsion field degree: $1440$
Full 152-torsion field degree: $7879680$

Models

This modular curve is isomorphic to $\mathbb{P}^1$.

Rational points

This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
$X_0(8)$ $8$ $2$ $2$ $0$ $0$
76.12.0.g.1 $76$ $2$ $2$ $0$ $?$
152.12.0.ba.1 $152$ $2$ $2$ $0$ $?$

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve Level Index Degree Genus
152.48.0.bg.1 $152$ $2$ $2$ $0$
152.48.0.bg.2 $152$ $2$ $2$ $0$
152.48.0.bh.1 $152$ $2$ $2$ $0$
152.48.0.bh.2 $152$ $2$ $2$ $0$
304.48.0.u.1 $304$ $2$ $2$ $0$
304.48.0.u.2 $304$ $2$ $2$ $0$
304.48.0.v.1 $304$ $2$ $2$ $0$
304.48.0.v.2 $304$ $2$ $2$ $0$
304.48.1.q.1 $304$ $2$ $2$ $1$
304.48.1.s.1 $304$ $2$ $2$ $1$
304.48.1.ce.1 $304$ $2$ $2$ $1$
304.48.1.cg.1 $304$ $2$ $2$ $1$