Invariants
| Level: | $312$ | $\SL_2$-level: | $24$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $1^{4}\cdot3^{4}\cdot8\cdot24$ | Cusp orbits | $1^{2}\cdot2^{4}$ | ||
| 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: | 24B0 |
Level structure
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 |
|---|---|---|---|---|---|
| $X_0(12)$ | $12$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 312.96.1.sd.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sd.3 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.se.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.se.3 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sh.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sh.3 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.si.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.si.3 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sl.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sl.3 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sm.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sm.3 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sp.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sp.4 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sq.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sq.4 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.st.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.st.4 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.su.2 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.su.4 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sx.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sx.3 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sy.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.sy.3 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.tb.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.tb.3 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.tc.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.tc.3 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.tf.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.tf.3 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.tg.1 | $312$ | $2$ | $2$ | $1$ |
| 312.96.1.tg.3 | $312$ | $2$ | $2$ | $1$ |
| 312.96.3.er.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.hp.2 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.ki.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.kk.2 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.lz.2 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.ma.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.ml.2 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.mm.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.qx.2 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.qy.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.rb.2 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.rc.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.rn.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.ro.2 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.rr.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.rs.2 | $312$ | $2$ | $2$ | $3$ |
| 312.144.3.g.1 | $312$ | $3$ | $3$ | $3$ |