accessibility Modular polynomials for the classpoly software package

This page provides modular polynomials Φ_ℓ(X,Y) between g(z) and g(z ⁄ ℓ) for various modular functions g(z) for primes ℓ < 200 that do not divide the level of g(z).

Each of the links below points to a compressed tarball that contains modular polynomials for a particular modular function. See Section 3 of the paper Class invariants by the CRT method for a description of each function (see Section 4.4 for the last two).

    j phi_j.tar     ɣ₂ phi_g2.tar     ƒ phi_f.tar     ƒ² phi_f2.tar     w₃¹² phi_w3.tar     w₅² phi_w5e2.tar     w₅⁶ phi_w5.tar     w₇⁴ phi_w7.tar     w₁₃² phi_w13.tar     w_2,3 phi_w2w3e1.tar     w_2,3² phi_w2w3e2.tar     w_2,3¹² phi_w2w3.tar     w_3,3 phi_w3w3e1.tar     w_3,3² phi_w3w3e2.tar     w_3,3⁶ phi_w3w3.tar     w_2,5 phi_w2w5e1.tar     w_2,5² phi_w2w5e2.tar     w_2,5⁶ phi_w2w5.tar     w_2,7 phi_w2w7e1.tar     w_2,7² phi_w2w7e2.tar     w_2,7⁴ phi_w2w7.tar     w_2,13 phi_w2w13e1.tar     w_2,13² phi_w2w13.tar     w_3,5 phi_w3w5e1.tar     w_3,5³ phi_w3w5.tar     w_3,7 phi_w3w7e1.tar     w_3,7² phi_w3w7.tar     w_3,13 phi_w3w13.tar     w_5,7 phi_w5w7.tar     A₃ phi_a3.tar     A₅ phi_a5.tar     A₇ phi_a7.tar     A₁₁ phi_a11.tar     A₁₃ phi_a13.tar     A₁₇ phi_a17.tar     A₁₉ phi_a19.tar     A₂₃ phi_a23.tar     A₂₉ phi_a29.tar     A₃₁ phi_a31.tar     A₄₁ phi_a41.tar     A₄₇ phi_a47.tar     A₅₉ phi_a59.tar     A₇₁ phi_a71.tar     t phi_t.tar     t² phi_t2.tar