The Jacobian variety of a smooth projective connected curve 
is the abelian variety 
parametrizing degree-zero line bundles. Its dimension
is the genus of 
.
For a chosen point 
,
the Abel-Jacobi map sends 
to 
. An elliptic curve
is its own Jacobian, with its identity as base point (Milne 2008).
Jacobian Variety
See also
Abelian Variety, Albanese Variety, Genus, Line Bundle, Picard VarietyExplore with Wolfram|Alpha
References
Milne, J. S. "Abelian Varieties." 2008. https://www.jmilne.org/math/CourseNotes/AV.pdf.Cite this as:
Weisstein, Eric W. "Jacobian Variety." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/JacobianVariety.html