The gonality of an algebraic curve 
over a field 
is the least degree of a nonconstant morphism 
, where 
is the projective line
and 
is smooth and projective,
and remains irreducible over an algebraic
closure of 
.
Equivalently, it is the least degree of a nonconstant element of its function
field 
(Derickx and van Hoeij 2014). The field is part of the
definition, since extending it can change the available maps.
This curve invariant motivates the analogous gonality
of a graph.
Maiti (2026) determined
 |
where 
is the modular curve parametrizing elliptic
curves with a point of order 42. The lower bound
uses exhaustive computations in the function field
over 
. Together with the finiteness of 
, the rational points of its Jacobian
variety, this shows that 
has only finitely many points of degree at most 11 over
and infinitely many of degree 12 over 
.
."
J. Algebra 417, 52-71, 2014. 
-Gonality
of 
Is 
."
9 Nov 2026.