Morton, Patrick2023-06-162023-06-162021-10Morton, P. (2021). The Hasse invariant of the Tate normal form E5 and the class number of Q(−5l). Journal of Number Theory, 227, 94–143. https://doi.org/10.1016/j.jnt.2021.03.0060022-314Xhttps://hdl.handle.net/1805/33827It is shown that the number of irreducible quartic factors of the form g(x)=x4+ax3+(11a+2)x2−ax+1 which divide the Hasse invariant of the Tate normal form E5 in characteristic l is a simple linear function of the class number h(−5l) of the field Q(−5l), when l≡2,3 modulo 5. A similar result holds for irreducible quadratic factors of g(x), when l≡1,4 modulo 5. This implies a formula for the number of linear factors over Fp of the supersingular polynomial ssp(5⁎)(x) corresponding to the Fricke group Γ0⁎(5).en-USPublisher PolicyClass equationClass field theoryFricke groupHasse invariantArticle