Properties

Label 276.48.0-276.h.1.1
Level $276$
Index $48$
Genus $0$
Cusps $6$
$\Q$-cusps $2$

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Invariants

Level: $276$ $\SL_2$-level: $4$
Index: $48$ $\PSL_2$-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 $4^{6}$ Cusp orbits $1^{2}\cdot4$
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: 4G0

Level structure

$\GL_2(\Z/276\Z)$-generators: $\begin{bmatrix}185&78\\74&41\end{bmatrix}$, $\begin{bmatrix}186&127\\95&238\end{bmatrix}$, $\begin{bmatrix}255&224\\164&35\end{bmatrix}$
Contains $-I$: no $\quad$ (see 276.24.0.h.1 for the level structure with $-I$)
Cyclic 276-isogeny field degree: $96$
Cyclic 276-torsion field degree: $8448$
Full 276-torsion field degree: $25648128$

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
12.24.0-4.d.1.2 $12$ $2$ $2$ $0$ $0$
92.24.0-4.d.1.1 $92$ $2$ $2$ $0$ $?$

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

Covering curve Level Index Degree Genus
276.144.4-276.bl.1.3 $276$ $3$ $3$ $4$
276.192.3-276.bi.1.6 $276$ $4$ $4$ $3$