Bjorn Poonen has contributed to these Knowls: $A$-field, $K$-gonality of a modular curve, Bézout determinant, Bézout matrix, Bézout matrix of a hypergeometric motive, CM field, CM points, Canonical field of definition of a modular curve, Cartan subgroup, Characteristic polynomial of an abelian variety over a finite field, Complex multiplication, Conductor of an abelian variety, Congruence subgroup, Cusps of a modular curve, Decomposition into isogeny factors, Dimension of an algebraic variety, Discriminant of a Shimura curve, Elliptic curve over a ring, Elliptic scheme, Endomorphism field, Euler factors at bad primes, Frobenius angles, Function fields of class number 1, Galois group of an isogeny class of abelian varieties, Genus of a modular curve, Genus of a smooth curve , Genus of a subgroup of $\GL_2$, Geometric component, Geometric components of a modular curve, Geometric gonality, Geometrically simple, Geometrically squarefree abelian variety, Gonality of a curve, Good and bad reduction, Honda-Tate theorem, Hyperelliptic curve, Index of a modular curve, Irreducible variety, Isogeny decomposition of the Jacobian of a modular curve, Isogeny of abelian varieties, Isomorphism classes within an isogeny class, Jacobian of a curve, Jacobian of a curve, L-polynomial of an abelian variety, Local L-factors at good primes, Modular cover, Modular curve, Modular curve $X(N)$, Modular curve $X_0(N)$, Modular curve $X_1(N)$, Modular curve $X_{\text{ns}}^{+}(N)$, Mordell-Weil group of an abelian variety, Non-singular point (definition), Potential good reduction, Principal homogeneous space, Rational points on a modular curve, Regulator of an abelian variety, Selmer group of an abelian variety, Shimura variety, Simple, Simple abelian variety, Smoothness of an algebraic curve, Squarefree abelian variety, Standard modular curves, Standard modular curves, Symplectic isomorphism, Tate-Shafarevich group, Theta divisor on a principally polarized abelian variety, Twist of an abelian variety, Upper half-plane, Weil polynomial, p-rank