Properties

Label 312.192.3-312.ql.1.13
Level $312$
Index $192$
Genus $3$
Cusps $12$
$\Q$-cusps $0$

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Invariants

Level: $312$ $\SL_2$-level: $24$ Newform level: $1$
Index: $192$ $\PSL_2$-index:$96$
Genus: $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$
Cusps: $12$ (none of which are rational) Cusp widths $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ Cusp orbits $2^{6}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2 \le \gamma \le 4$
$\overline{\Q}$-gonality: $2 \le \gamma \le 3$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 24V3

Level structure

$\GL_2(\Z/312\Z)$-generators: $\begin{bmatrix}61&192\\112&35\end{bmatrix}$, $\begin{bmatrix}117&131\\128&291\end{bmatrix}$, $\begin{bmatrix}165&238\\32&205\end{bmatrix}$, $\begin{bmatrix}171&19\\44&61\end{bmatrix}$, $\begin{bmatrix}227&247\\276&157\end{bmatrix}$
Contains $-I$: no $\quad$ (see 312.96.3.ql.1 for the level structure with $-I$)
Cyclic 312-isogeny field degree: $28$
Cyclic 312-torsion field degree: $1344$
Full 312-torsion field degree: $10063872$

Rational points

This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
24.96.1-24.ix.1.22 $24$ $2$ $2$ $1$ $0$
312.48.0-312.ef.1.5 $312$ $4$ $4$ $0$ $?$
312.96.1-156.p.1.2 $312$ $2$ $2$ $1$ $?$
312.96.1-156.p.1.22 $312$ $2$ $2$ $1$ $?$
312.96.1-24.ix.1.26 $312$ $2$ $2$ $1$ $?$
312.96.1-312.zz.1.9 $312$ $2$ $2$ $1$ $?$
312.96.1-312.zz.1.28 $312$ $2$ $2$ $1$ $?$

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

Covering curve Level Index Degree Genus
312.384.5-312.bds.1.5 $312$ $2$ $2$ $5$
312.384.5-312.bds.2.3 $312$ $2$ $2$ $5$
312.384.5-312.bds.3.9 $312$ $2$ $2$ $5$
312.384.5-312.bds.4.5 $312$ $2$ $2$ $5$
312.384.5-312.bdw.1.5 $312$ $2$ $2$ $5$
312.384.5-312.bdw.2.2 $312$ $2$ $2$ $5$
312.384.5-312.bdw.3.9 $312$ $2$ $2$ $5$
312.384.5-312.bdw.4.3 $312$ $2$ $2$ $5$
312.384.5-312.bkm.1.5 $312$ $2$ $2$ $5$
312.384.5-312.bkm.2.3 $312$ $2$ $2$ $5$
312.384.5-312.bkm.3.9 $312$ $2$ $2$ $5$
312.384.5-312.bkm.4.5 $312$ $2$ $2$ $5$
312.384.5-312.bkq.1.5 $312$ $2$ $2$ $5$
312.384.5-312.bkq.2.5 $312$ $2$ $2$ $5$
312.384.5-312.bkq.3.9 $312$ $2$ $2$ $5$
312.384.5-312.bkq.4.9 $312$ $2$ $2$ $5$