Invariants
Level: | $312$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot3^{2}\cdot6\cdot8\cdot24$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24G1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}18&175\\79&246\end{bmatrix}$, $\begin{bmatrix}39&278\\58&263\end{bmatrix}$, $\begin{bmatrix}107&276\\6&293\end{bmatrix}$, $\begin{bmatrix}189&50\\184&11\end{bmatrix}$, $\begin{bmatrix}296&19\\299&288\end{bmatrix}$, $\begin{bmatrix}296&115\\179&228\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.48.1.zu.1 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $28$ |
Cyclic 312-torsion field degree: | $2688$ |
Full 312-torsion field degree: | $20127744$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.48.0-12.g.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
312.24.0-104.y.1.3 | $312$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
312.48.0-12.g.1.16 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
312.192.1-312.rb.1.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.rb.2.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.rb.3.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.rb.4.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.rd.1.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.rd.2.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.rd.3.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.rd.4.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.sl.1.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.sl.2.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.sl.3.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.sl.4.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.sn.1.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.sn.2.13 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.sn.3.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.sn.4.25 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.3-312.gc.1.69 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.hq.1.17 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.jg.1.26 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ji.1.17 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.lu.1.25 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.lw.1.17 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.mg.1.29 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.mi.1.17 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.oc.1.3 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.of.1.33 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ox.1.7 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.oy.1.17 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.pq.1.26 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.pt.1.17 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.pz.1.30 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.qa.1.17 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.si.1.13 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.si.2.13 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.si.3.25 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.si.4.25 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.sk.1.13 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.sk.2.13 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.sk.3.25 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.sk.4.25 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.tg.1.13 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.tg.2.13 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.tg.3.25 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.tg.4.25 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ti.1.13 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ti.2.13 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ti.3.25 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.192.3-312.ti.4.25 | $312$ | $2$ | $2$ | $3$ | $?$ | not computed |
312.288.5-312.pc.1.23 | $312$ | $3$ | $3$ | $5$ | $?$ | not computed |