Properties

Label 80.288.7-80.bs.2.3
Level $80$
Index $288$
Genus $7$
Cusps $12$
$\Q$-cusps $8$

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Invariants

Level: $80$ $\SL_2$-level: $80$ Newform level: $1$
Index: $288$ $\PSL_2$-index:$144$
Genus: $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$
Cusps: $12$ (of which $8$ are rational) Cusp widths $1^{2}\cdot2^{3}\cdot5^{2}\cdot10^{3}\cdot16\cdot80$ Cusp orbits $1^{8}\cdot2^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $3 \le \gamma \le 7$
$\overline{\Q}$-gonality: $3 \le \gamma \le 7$
Rational cusps: $8$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 80H7

Level structure

$\GL_2(\Z/80\Z)$-generators: $\begin{bmatrix}5&8\\36&57\end{bmatrix}$, $\begin{bmatrix}7&62\\46&23\end{bmatrix}$, $\begin{bmatrix}10&19\\9&20\end{bmatrix}$, $\begin{bmatrix}26&37\\79&24\end{bmatrix}$, $\begin{bmatrix}29&8\\36&1\end{bmatrix}$, $\begin{bmatrix}78&75\\7&66\end{bmatrix}$
Contains $-I$: no $\quad$ (see 80.144.7.bs.2 for the level structure with $-I$)
Cyclic 80-isogeny field degree: $2$
Cyclic 80-torsion field degree: $32$
Full 80-torsion field degree: $40960$

Rational points

This modular curve has 8 rational cusps but no known non-cuspidal rational points.

Modular covers

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve Level Index Degree Genus Rank
$X_0(5)$ $5$ $48$ $24$ $0$ $0$
16.48.0-16.e.2.3 $16$ $6$ $6$ $0$ $0$

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
16.48.0-16.e.2.3 $16$ $6$ $6$ $0$ $0$
40.144.3-40.bx.1.30 $40$ $2$ $2$ $3$ $0$
80.144.3-40.bx.1.18 $80$ $2$ $2$ $3$ $?$