Szpiro's conjecture: for any ε > 0 {\displaystyle \varepsilon >0} {\displaystyle \varepsilon >0}, there is some constant C ( ε ) {\displaystyle C(\varepsilon )} {\displaystyle C(\varepsilon )} such that, for any elliptic curve E {\displaystyle E} {\displaystyle E} defined over Q {\displaystyle \mathbb {Q} } {\displaystyle \mathbb {Q} } with minimal discriminant Δ {\displaystyle \Delta } {\displaystyle \Delta } and conductor f {\displaystyle f} {\displaystyle f}, we have | Δ | ≤ C ( ε ) ⋅ f 6 + ε {\displaystyle |\Delta |\leq C(\varepsilon )\cdot f^{6+\varepsilon }} {\displaystyle |\Delta |\leq C(\varepsilon )\cdot f^{6+\varepsilon }}.
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Source status
Open
Field
Number theory · Arithmetic geometry
Record type
Revision-pinned source placement
Verification
Source-index reviewed
Source grade
secondary
Reviewed
2026-07-27T18:04:33.834Z
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Source trail
Wikipedia list subsection — Exact Number theory › Arithmetic geometry subsection in the revision-pinned source.
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