Properties

Label 152.24.0-76.h.1.5
Level $152$
Index $24$
Genus $0$
Cusps $4$
$\Q$-cusps $2$

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Invariants

Level: $152$ $\SL_2$-level: $8$
Index: $24$ $\PSL_2$-index:$12$
Genus: $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$
Cusps: $4$ (of which $2$ are rational) Cusp widths $2^{2}\cdot4^{2}$ Cusp orbits $1^{2}\cdot2$
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: 4E0

Level structure

$\GL_2(\Z/152\Z)$-generators: $\begin{bmatrix}33&60\\62&147\end{bmatrix}$, $\begin{bmatrix}33&88\\49&19\end{bmatrix}$, $\begin{bmatrix}61&48\\23&89\end{bmatrix}$, $\begin{bmatrix}123&12\\142&67\end{bmatrix}$
Contains $-I$: no $\quad$ (see 76.12.0.h.1 for the level structure with $-I$)
Cyclic 152-isogeny field degree: $40$
Cyclic 152-torsion field degree: $2880$
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
8.12.0-4.c.1.6 $8$ $2$ $2$ $0$ $0$
152.12.0-4.c.1.6 $152$ $2$ $2$ $0$ $?$

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

Covering curve Level Index Degree Genus
152.480.17-76.l.1.7 $152$ $20$ $20$ $17$
152.48.0-152.bi.1.2 $152$ $2$ $2$ $0$
152.48.0-152.bi.1.8 $152$ $2$ $2$ $0$
152.48.0-152.bj.1.7 $152$ $2$ $2$ $0$
152.48.0-152.bj.1.12 $152$ $2$ $2$ $0$
152.48.0-152.bq.1.4 $152$ $2$ $2$ $0$
152.48.0-152.bq.1.6 $152$ $2$ $2$ $0$
152.48.0-152.br.1.4 $152$ $2$ $2$ $0$
152.48.0-152.br.1.8 $152$ $2$ $2$ $0$