Invariants
Level: | $312$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{2}$ | Cusp orbits | $2^{3}\cdot4$ | ||
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: | 8N0 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}11&2\\20&153\end{bmatrix}$, $\begin{bmatrix}103&60\\248&289\end{bmatrix}$, $\begin{bmatrix}157&128\\84&295\end{bmatrix}$, $\begin{bmatrix}199&230\\4&309\end{bmatrix}$, $\begin{bmatrix}211&70\\292&149\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.48.0.bd.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $112$ |
Cyclic 312-torsion field degree: | $10752$ |
Full 312-torsion field degree: | $20127744$ |
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 |
---|---|---|---|---|---|
24.48.0-24.i.1.28 | $24$ | $2$ | $2$ | $0$ | $0$ |
104.48.0-104.h.1.22 | $104$ | $2$ | $2$ | $0$ | $?$ |
312.48.0-156.c.1.7 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.48.0-156.c.1.23 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.48.0-104.h.1.16 | $312$ | $2$ | $2$ | $0$ | $?$ |
312.48.0-24.i.1.8 | $312$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
312.192.1-312.r.2.10 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.cv.2.16 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.dw.2.14 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.ee.2.14 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.ix.2.16 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.jf.2.13 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.jm.2.14 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.ju.2.14 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.ms.2.12 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.na.2.12 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.nj.2.4 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.nr.2.16 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.pe.2.12 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.pm.2.12 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.ps.2.16 | $312$ | $2$ | $2$ | $1$ |
312.192.1-312.pw.2.10 | $312$ | $2$ | $2$ | $1$ |
312.288.8-312.dm.1.54 | $312$ | $3$ | $3$ | $8$ |
312.384.7-312.di.2.44 | $312$ | $4$ | $4$ | $7$ |