Invariants
Level: | -level: | ||||||
Index: | -index: | ||||||
Genus: | |||||||
Cusps: | (of which are rational) | Cusp widths | Cusp orbits | ||||
Elliptic points: | of order and of order | ||||||
-gonality: | |||||||
-gonality: | |||||||
Rational cusps: | |||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16G0 |
Rouse and Zureick-Brown (RZB) label: | X217c |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 16.96.0.137 |
Level structure
-generators: | , , |
-subgroup: | |
Contains : | no (see 16.48.0.e.1 for the level structure with ) |
Cyclic 16-isogeny field degree: | |
Cyclic 16-torsion field degree: | |
Full 16-torsion field degree: |
Models
This modular curve is isomorphic to .
Rational points
This modular curve has infinitely many rational points, including 7 stored non-cuspidal points.
Maps to other modular curves
-invariant map of degree 48 to the modular curve :
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.48.0-8.k.1.6 | |||||
16.48.0-16.e.1.3 | |||||
16.48.0-16.e.1.6 | |||||
16.48.0-16.e.2.5 | |||||
16.48.0-16.e.2.11 | |||||
16.48.0-8.k.1.4 |
This modular curve is minimally covered by the modular curves in the database listed below.