# Heegner's lemma

In mathematics, Heegner's lemma is a lemma used by Kurt Heegner in his paper on the class number problem. His lemma states that if

${\displaystyle y^{2}=a_{4}x^{4}+a_{3}x^{3}+a_{2}x^{2}+a_{1}x+a_{0}}$

is a curve over a field with a4 not a square, then it has a solution if it has a solution in an extension of odd degree.

## References

• Birch, Bryan (2004), "Heegner points: the beginnings", in Darmon, Henri; Zhang, Shou-Wu (eds.), Heegner points and Rankin L-series, Math. Sci. Res. Inst. Publ., 49, Cambridge University Press, pp. 1–10, CiteSeerX 10.1.1.231.4662, doi:10.1017/CBO9780511756375.002, ISBN 978-0-521-83659-3, MR 2083207