Limits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryElliptic curves are central to number theory — they were key to Andrew Wiles' proof of Fermat's Last Theorem and underpin widely used cryptographic systems. This conjecture, formulated in the 1960s from numerical experiments, predicts a precise link between how many rational-number solutions an elliptic curve has and the behavior of a related complex analytic function at a single point. It remains one of the deepest open questions about when polynomial equations have rational solutions.
The question, scope, and sources behind this Registry record.
For an elliptic curve E over ℚ, the rank of the group of rational points E(ℚ) equals the order of vanishing of the associated L-function L(E, s) at s = 1.
Change a parameter to stress-test whether a proposed result is still inside the published specification. This is an audit aid, not a proof checker.
This record has no editable parameters. Read the formal question and assumptions before challenging it.
Current frontiers derived from accepted Claims.
The frontier is not sacred
Most progress starts with a disagreement that survives contact with evidence. If you can push the known lower bound up or pull the upper bound down, show us the work.
≥ when you have shown that at least this value is achievable.≤ when you have shown that anything above this value is impossible.No vibes. State the value, define the scope, and link the paper, proof, code, or reproduction that lets another person check it. Editors review every challenge before the public record changes.
Challenge this recordAssertions tied to evidence, attribution, and review.
No accepted Claims are recorded for this Limit yet.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.