Invariants
Level: | $312$ | $\SL_2$-level: | $8$ | 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 $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G1 |
Level structure
$\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}67&78\\264&193\end{bmatrix}$, $\begin{bmatrix}85&268\\256&201\end{bmatrix}$, $\begin{bmatrix}117&58\\220&35\end{bmatrix}$, $\begin{bmatrix}155&50\\88&161\end{bmatrix}$, $\begin{bmatrix}217&122\\276&89\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 312.48.1.ef.2 for the level structure with $-I$) |
Cyclic 312-isogeny field degree: | $112$ |
Cyclic 312-torsion field degree: | $10752$ |
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 |
---|---|---|---|---|---|---|
8.48.0-8.e.1.15 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
312.48.0-8.e.1.3 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.0-312.t.2.2 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.0-312.t.2.36 | $312$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
312.48.1-312.d.1.11 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.48.1-312.d.1.26 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
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.ba.2.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.cy.1.9 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.ep.1.12 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.ex.2.4 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.ii.1.10 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.iq.2.3 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.kf.2.6 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.kn.1.12 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.me.2.1 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.mm.1.9 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.ob.1.15 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.oj.2.7 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.pg.1.10 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.po.2.5 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qb.2.11 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.192.1-312.qf.1.14 | $312$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
312.288.9-312.tn.2.18 | $312$ | $3$ | $3$ | $9$ | $?$ | not computed |
312.384.9-312.kp.2.8 | $312$ | $4$ | $4$ | $9$ | $?$ | not computed |