Invariants
Level: | $76$ | $\SL_2$-level: | $4$ | ||||
Index: | $12$ | $\PSL_2$-index: | $12$ | ||||
Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}$ | Cusp orbits | $2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 4E0 |
Level structure
$\GL_2(\Z/76\Z)$-generators: | $\begin{bmatrix}3&28\\20&5\end{bmatrix}$, $\begin{bmatrix}21&30\\19&49\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 76-isogeny field degree: | $40$ |
Cyclic 76-torsion field degree: | $1440$ |
Full 76-torsion field degree: | $984960$ |
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 |
---|---|---|---|---|---|
4.6.0.d.1 | $4$ | $2$ | $2$ | $0$ | $0$ |
38.6.0.b.1 | $38$ | $2$ | $2$ | $0$ | $0$ |
76.6.0.c.1 | $76$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
76.240.17.m.1 | $76$ | $20$ | $20$ | $17$ |
152.24.1.q.1 | $152$ | $2$ | $2$ | $1$ |
152.24.1.s.1 | $152$ | $2$ | $2$ | $1$ |
152.24.1.dc.1 | $152$ | $2$ | $2$ | $1$ |
152.24.1.de.1 | $152$ | $2$ | $2$ | $1$ |
228.36.2.fi.1 | $228$ | $3$ | $3$ | $2$ |
228.48.1.bo.1 | $228$ | $4$ | $4$ | $1$ |