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Properties

Label 152.48.0.i.2
Level $152$
Index $48$
Genus $0$
Cusps $10$
$\Q$-cusps $2$

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Invariants

Level: $152$ $\SL_2$-level: $8$
Index: $48$ $\PSL_2$-index:$48$
Genus: $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$
Cusps: $10$ (of which $2$ are rational) Cusp widths $4^{8}\cdot8^{2}$ Cusp orbits $1^{2}\cdot2^{2}\cdot4$
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: 8N0

Level structure

$\GL_2(\Z/152\Z)$-generators: $\begin{bmatrix}1&36\\138&49\end{bmatrix}$, $\begin{bmatrix}103&40\\66&119\end{bmatrix}$, $\begin{bmatrix}103&132\\26&79\end{bmatrix}$, $\begin{bmatrix}113&104\\2&19\end{bmatrix}$, $\begin{bmatrix}137&112\\40&71\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 152.96.0-152.i.2.1, 152.96.0-152.i.2.2, 152.96.0-152.i.2.3, 152.96.0-152.i.2.4, 152.96.0-152.i.2.5, 152.96.0-152.i.2.6, 152.96.0-152.i.2.7, 152.96.0-152.i.2.8, 152.96.0-152.i.2.9, 152.96.0-152.i.2.10, 152.96.0-152.i.2.11, 152.96.0-152.i.2.12, 152.96.0-152.i.2.13, 152.96.0-152.i.2.14, 152.96.0-152.i.2.15, 152.96.0-152.i.2.16
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 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
8.24.0.e.1 $8$ $2$ $2$ $0$ $0$
76.24.0.c.1 $76$ $2$ $2$ $0$ $?$
152.24.0.h.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
152.96.1.i.1 $152$ $2$ $2$ $1$
152.96.1.y.1 $152$ $2$ $2$ $1$
152.96.1.bc.1 $152$ $2$ $2$ $1$
152.96.1.bg.1 $152$ $2$ $2$ $1$
152.96.1.bu.1 $152$ $2$ $2$ $1$
152.96.1.by.1 $152$ $2$ $2$ $1$
152.96.1.cb.1 $152$ $2$ $2$ $1$
152.96.1.cd.1 $152$ $2$ $2$ $1$