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Properties

Label 296.12.0.v.1
Level $296$
Index $12$
Genus $0$
Cusps $4$
$\Q$-cusps $2$

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Invariants

Level: $296$ $\SL_2$-level: $4$
Index: $12$ $\PSL_2$-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: $\begin{bmatrix}3&184\\107&115\end{bmatrix}$, $\begin{bmatrix}41&256\\236&59\end{bmatrix}$, $\begin{bmatrix}169&136\\176&13\end{bmatrix}$, $\begin{bmatrix}189&188\\166&21\end{bmatrix}$, $\begin{bmatrix}271&216\\264&243\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 296.24.0-296.v.1.1, 296.24.0-296.v.1.2, 296.24.0-296.v.1.3, 296.24.0-296.v.1.4, 296.24.0-296.v.1.5, 296.24.0-296.v.1.6, 296.24.0-296.v.1.7, 296.24.0-296.v.1.8
Cyclic 296-isogeny field degree: $76$
Cyclic 296-torsion field degree: $10944$
Full 296-torsion field degree: $233238528$

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
$X_0(4)$ $4$ $2$ $2$ $0$ $0$
296.6.0.b.1 $296$ $2$ $2$ $0$ $?$
296.6.0.f.1 $296$ $2$ $2$ $0$ $?$

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

Covering curve Level Index Degree Genus
296.24.0.bo.1 $296$ $2$ $2$ $0$
296.24.0.bp.1 $296$ $2$ $2$ $0$
296.24.0.by.1 $296$ $2$ $2$ $0$
296.24.0.bz.1 $296$ $2$ $2$ $0$