Invariants
Level: | $276$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $4 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $12^{6}$ | Cusp orbits | $2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 6$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 4$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12C4 |
Level structure
$\GL_2(\Z/276\Z)$-generators: | $\begin{bmatrix}73&208\\52&53\end{bmatrix}$, $\begin{bmatrix}187&50\\92&17\end{bmatrix}$, $\begin{bmatrix}239&68\\214&179\end{bmatrix}$, $\begin{bmatrix}263&42\\222&31\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 276.72.4.t.1 for the level structure with $-I$) |
Cyclic 276-isogeny field degree: | $192$ |
Cyclic 276-torsion field degree: | $8448$ |
Full 276-torsion field degree: | $8549376$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
12.72.2-12.d.1.3 | $12$ | $2$ | $2$ | $2$ | $0$ |
276.72.2-12.d.1.4 | $276$ | $2$ | $2$ | $2$ | $?$ |
276.72.2-276.e.1.3 | $276$ | $2$ | $2$ | $2$ | $?$ |
276.72.2-276.e.1.7 | $276$ | $2$ | $2$ | $2$ | $?$ |
276.72.2-276.h.1.2 | $276$ | $2$ | $2$ | $2$ | $?$ |
276.72.2-276.h.1.10 | $276$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
276.288.7-276.k.1.4 | $276$ | $2$ | $2$ | $7$ |
276.288.7-276.n.1.6 | $276$ | $2$ | $2$ | $7$ |
276.288.7-276.s.1.1 | $276$ | $2$ | $2$ | $7$ |
276.288.7-276.t.1.1 | $276$ | $2$ | $2$ | $7$ |
276.288.7-276.bk.1.7 | $276$ | $2$ | $2$ | $7$ |
276.288.7-276.bo.1.6 | $276$ | $2$ | $2$ | $7$ |
276.288.7-276.cf.1.2 | $276$ | $2$ | $2$ | $7$ |
276.288.7-276.ch.1.2 | $276$ | $2$ | $2$ | $7$ |