= Grössencharacter of the square-lattice elliptic curve
{c}
{title2=$\psi_E(\mathfrak a)=\text{the primary generator of }\mathfrak a$}
For $E:y^2=x^3-x$ over $\mathbb Q(i)$, the <Hecke character> has conductor $(1+i)^3$ and ideal infinity type $(1,0)$. Its value on an ideal prime to $2$ is its unique <primary Gaussian integer> generator. Rational $(1+i)^3$-torsion fixes the unit ambiguity of the Frobenius value. At a split prime $\mathfrak p$, its value reduces to the degree-$p$ <Frobenius isogeny>; at an inert rational prime $p$, its value is $-p$, reducing to the $p^2$-power <Frobenius isogeny>.
Back to article page
