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Properties

Label 88.24.0.bv.2
Level $88$
Index $24$
Genus $0$
Cusps $6$
$\Q$-cusps $2$

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Invariants

Level: $88$ $\SL_2$-level: $8$
Index: $24$ $\PSL_2$-index:$24$
Genus: $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps: $6$ (of which $2$ are rational) Cusp widths $1^{2}\cdot2\cdot4\cdot8^{2}$ Cusp orbits $1^{2}\cdot2^{2}$
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: 8I0

Level structure

$\GL_2(\Z/88\Z)$-generators: $\begin{bmatrix}24&1\\71&10\end{bmatrix}$, $\begin{bmatrix}26&25\\19&32\end{bmatrix}$, $\begin{bmatrix}34&59\\63&78\end{bmatrix}$, $\begin{bmatrix}51&4\\72&87\end{bmatrix}$, $\begin{bmatrix}85&10\\62&49\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 88.48.0-88.bv.2.1, 88.48.0-88.bv.2.2, 88.48.0-88.bv.2.3, 88.48.0-88.bv.2.4, 88.48.0-88.bv.2.5, 88.48.0-88.bv.2.6, 88.48.0-88.bv.2.7, 88.48.0-88.bv.2.8, 88.48.0-88.bv.2.9, 88.48.0-88.bv.2.10, 88.48.0-88.bv.2.11, 88.48.0-88.bv.2.12, 88.48.0-88.bv.2.13, 88.48.0-88.bv.2.14, 88.48.0-88.bv.2.15, 88.48.0-88.bv.2.16, 176.48.0-88.bv.2.1, 176.48.0-88.bv.2.2, 176.48.0-88.bv.2.3, 176.48.0-88.bv.2.4, 176.48.0-88.bv.2.5, 176.48.0-88.bv.2.6, 176.48.0-88.bv.2.7, 176.48.0-88.bv.2.8, 176.48.0-88.bv.2.9, 176.48.0-88.bv.2.10, 176.48.0-88.bv.2.11, 176.48.0-88.bv.2.12, 176.48.0-88.bv.2.13, 176.48.0-88.bv.2.14, 176.48.0-88.bv.2.15, 176.48.0-88.bv.2.16, 264.48.0-88.bv.2.1, 264.48.0-88.bv.2.2, 264.48.0-88.bv.2.3, 264.48.0-88.bv.2.4, 264.48.0-88.bv.2.5, 264.48.0-88.bv.2.6, 264.48.0-88.bv.2.7, 264.48.0-88.bv.2.8, 264.48.0-88.bv.2.9, 264.48.0-88.bv.2.10, 264.48.0-88.bv.2.11, 264.48.0-88.bv.2.12, 264.48.0-88.bv.2.13, 264.48.0-88.bv.2.14, 264.48.0-88.bv.2.15, 264.48.0-88.bv.2.16
Cyclic 88-isogeny field degree: $12$
Cyclic 88-torsion field degree: $480$
Full 88-torsion field degree: $844800$

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
$X_0(8)$ $8$ $2$ $2$ $0$ $0$

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

Covering curve Level Index Degree Genus
88.48.0.bb.2 $88$ $2$ $2$ $0$
88.48.0.bc.1 $88$ $2$ $2$ $0$
88.48.0.bd.1 $88$ $2$ $2$ $0$
88.48.0.bf.1 $88$ $2$ $2$ $0$
88.48.0.bh.1 $88$ $2$ $2$ $0$
88.48.0.bi.1 $88$ $2$ $2$ $0$
88.48.0.bk.2 $88$ $2$ $2$ $0$
88.48.0.bn.1 $88$ $2$ $2$ $0$
88.288.19.ft.2 $88$ $12$ $12$ $19$
176.48.0.bd.2 $176$ $2$ $2$ $0$
176.48.0.bj.2 $176$ $2$ $2$ $0$
176.48.0.bl.1 $176$ $2$ $2$ $0$
176.48.0.br.2 $176$ $2$ $2$ $0$
176.48.0.bt.2 $176$ $2$ $2$ $0$
176.48.0.bv.2 $176$ $2$ $2$ $0$
176.48.0.bx.1 $176$ $2$ $2$ $0$
176.48.0.bz.2 $176$ $2$ $2$ $0$
176.48.1.bh.2 $176$ $2$ $2$ $1$
176.48.1.bj.1 $176$ $2$ $2$ $1$
176.48.1.bl.2 $176$ $2$ $2$ $1$
176.48.1.bn.2 $176$ $2$ $2$ $1$
176.48.1.bp.2 $176$ $2$ $2$ $1$
176.48.1.bv.1 $176$ $2$ $2$ $1$
176.48.1.bx.2 $176$ $2$ $2$ $1$
176.48.1.cd.2 $176$ $2$ $2$ $1$
264.48.0.df.1 $264$ $2$ $2$ $0$
264.48.0.dh.2 $264$ $2$ $2$ $0$
264.48.0.dj.1 $264$ $2$ $2$ $0$
264.48.0.dl.2 $264$ $2$ $2$ $0$
264.48.0.eb.1 $264$ $2$ $2$ $0$
264.48.0.ee.2 $264$ $2$ $2$ $0$
264.48.0.ei.1 $264$ $2$ $2$ $0$
264.48.0.en.2 $264$ $2$ $2$ $0$
264.72.4.nv.2 $264$ $3$ $3$ $4$
264.96.3.pk.2 $264$ $4$ $4$ $3$