Surjectivity conjecture for the minimal isogeny degree on primes

Less than 1 year old · traced to

Let P\mathbb{P} be the set of prime numbers, and let δ ⁣:P→Z>0\delta\colon\mathbb{P}\to\mathbb{Z}_{>0} assign to each prime pp the value δ(p)\delta(p). Prime-value surjectivity conjecture. For every n∈Z>0n\in\mathbb{Z}_{>0}, there exists a prime p∈Pp\in\mathbb{P} with δ(p)=n\delta(p)=n, equivalently,

Im⁡(δ)=Z>0.\operatorname{Im}(\delta)=\mathbb{Z}_{>0}.

Thus every positive integer should occur as the value of δ(p)\delta(p) for some prime. The paper verifies this numerically for all n≤50n\leq50, but the assertion for all positive integers remains open.

References

Primary source

Yves Aubry, Roger Oyono and Christelle Vincent, “Minimal degree of an isogeny between a supersingular elliptic curve and its conjugate”, arXiv:2607.14624 (2026).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.