Denominator conjecture for modular polynomials in the b'-invariants
Denominator conjecture for modular polynomials in the b'-invariants
Let , and let be a polynomial describing the locus of principally polarized abelian surfaces modulo that are -isogenous to a principally polarized abelian surface which is isogenous to a product of two elliptic curves by the -isogeny and satisfies .
Denominator conjecture. The polynomial is the denominator of every coefficient of the three modular polynomials in the functions .
The preceding proposition shows that the denominators are divisible by a polynomial describing this locus, and computations for support the assertion that the same polynomial is the denominator for all coefficients. The source does not state a resolution status.
Sources & referencesView supporting material
Primary source
Enea Milio, “A quasi-linear time algorithm for computing modular polynomials in dimension 2”, arXiv:1411.0409 (2015).
Progress summary
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