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Properties

Label 304.96.2.d.1
Level $304$
Index $96$
Genus $2$
Cusps $14$
$\Q$-cusps $2$

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Invariants

Level: $304$ $\SL_2$-level: $16$ Newform level: $1$
Index: $96$ $\PSL_2$-index:$96$
Genus: $2 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 14 }{2}$
Cusps: $14$ (of which $2$ are rational) Cusp widths $4^{8}\cdot8^{4}\cdot16^{2}$ Cusp orbits $1^{2}\cdot2^{4}\cdot4$
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: 16I2

Level structure

$\GL_2(\Z/304\Z)$-generators: $\begin{bmatrix}17&28\\160&177\end{bmatrix}$, $\begin{bmatrix}41&260\\100&45\end{bmatrix}$, $\begin{bmatrix}57&40\\148&259\end{bmatrix}$, $\begin{bmatrix}201&136\\88&131\end{bmatrix}$, $\begin{bmatrix}233&104\\180&57\end{bmatrix}$, $\begin{bmatrix}263&64\\116&21\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 304.192.2-304.d.1.1, 304.192.2-304.d.1.2, 304.192.2-304.d.1.3, 304.192.2-304.d.1.4, 304.192.2-304.d.1.5, 304.192.2-304.d.1.6, 304.192.2-304.d.1.7, 304.192.2-304.d.1.8, 304.192.2-304.d.1.9, 304.192.2-304.d.1.10, 304.192.2-304.d.1.11, 304.192.2-304.d.1.12, 304.192.2-304.d.1.13, 304.192.2-304.d.1.14, 304.192.2-304.d.1.15, 304.192.2-304.d.1.16, 304.192.2-304.d.1.17, 304.192.2-304.d.1.18, 304.192.2-304.d.1.19, 304.192.2-304.d.1.20, 304.192.2-304.d.1.21, 304.192.2-304.d.1.22, 304.192.2-304.d.1.23, 304.192.2-304.d.1.24, 304.192.2-304.d.1.25, 304.192.2-304.d.1.26, 304.192.2-304.d.1.27, 304.192.2-304.d.1.28, 304.192.2-304.d.1.29, 304.192.2-304.d.1.30, 304.192.2-304.d.1.31, 304.192.2-304.d.1.32
Cyclic 304-isogeny field degree: $80$
Cyclic 304-torsion field degree: $5760$
Full 304-torsion field degree: $31518720$

Rational points

This modular curve has 2 rational cusps but no known non-cuspidal rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
8.48.0.c.1 $8$ $2$ $2$ $0$ $0$

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

Covering curve Level Index Degree Genus
304.192.5.p.1 $304$ $2$ $2$ $5$
304.192.5.p.2 $304$ $2$ $2$ $5$
304.192.5.t.1 $304$ $2$ $2$ $5$
304.192.5.t.2 $304$ $2$ $2$ $5$
304.192.5.bo.1 $304$ $2$ $2$ $5$
304.192.5.bo.4 $304$ $2$ $2$ $5$
304.192.5.bs.1 $304$ $2$ $2$ $5$
304.192.5.bs.2 $304$ $2$ $2$ $5$
304.192.5.cx.1 $304$ $2$ $2$ $5$
304.192.5.cx.2 $304$ $2$ $2$ $5$
304.192.5.cz.1 $304$ $2$ $2$ $5$
304.192.5.cz.2 $304$ $2$ $2$ $5$
304.192.5.dd.1 $304$ $2$ $2$ $5$
304.192.5.dd.2 $304$ $2$ $2$ $5$
304.192.5.dh.1 $304$ $2$ $2$ $5$
304.192.5.dh.2 $304$ $2$ $2$ $5$
304.192.7.l.1 $304$ $2$ $2$ $7$
304.192.7.n.1 $304$ $2$ $2$ $7$
304.192.7.q.1 $304$ $2$ $2$ $7$
304.192.7.t.1 $304$ $2$ $2$ $7$
304.192.7.bc.1 $304$ $2$ $2$ $7$
304.192.7.bd.1 $304$ $2$ $2$ $7$
304.192.7.bh.1 $304$ $2$ $2$ $7$
304.192.7.bj.1 $304$ $2$ $2$ $7$