Properties

Label 296.24.0-296.v.1.8
Level $296$
Index $24$
Genus $0$
Cusps $4$
$\Q$-cusps $2$

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Invariants

Level: $296$ $\SL_2$-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

$\GL_2(\Z/296\Z)$-generators: $\begin{bmatrix}73&232\\288&19\end{bmatrix}$, $\begin{bmatrix}203&168\\119&123\end{bmatrix}$, $\begin{bmatrix}229&40\\161&177\end{bmatrix}$, $\begin{bmatrix}241&92\\175&93\end{bmatrix}$
Contains $-I$: no $\quad$ (see 296.12.0.v.1 for the level structure with $-I$)
Cyclic 296-isogeny field degree: $76$
Cyclic 296-torsion field degree: $10944$
Full 296-torsion field degree: $116619264$

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 $8$ $2$ $2$ $0$ $0$
296.12.0-4.c.1.5 $296$ $2$ $2$ $0$ $?$

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

Covering curve Level Index Degree Genus
296.48.0-296.bo.1.6 $296$ $2$ $2$ $0$
296.48.0-296.bo.1.8 $296$ $2$ $2$ $0$
296.48.0-296.bp.1.6 $296$ $2$ $2$ $0$
296.48.0-296.bp.1.8 $296$ $2$ $2$ $0$
296.48.0-296.by.1.6 $296$ $2$ $2$ $0$
296.48.0-296.by.1.8 $296$ $2$ $2$ $0$
296.48.0-296.bz.1.6 $296$ $2$ $2$ $0$
296.48.0-296.bz.1.8 $296$ $2$ $2$ $0$