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curve #4311

y² + xy + y = x³ − x² − 2667476x + 43710086

a-invariants: [1, -1, 1, -2667476, 43710086]
c-invariants: [128038833, -37189339785]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 224236676260701
discriminant (Δ): 1213934173468542493929
Faltings height: 2.7352
naive height: 56.0035 ☆ record for ℤ/2ℤ torsion, rank ≥ 7
primes of bad reduction: 3, 13, 23, 61, 127, 757, 1093
regulator: 12642.34511235206696482051961964058117327478624803982
submitted by: Volkan Dagli
submitted at: 2026-10-17 09:49:42 UTC
last updated: 2026-10-17 09:49:42 UTC

Witness: 7 independent points log in to add more points →

(-1628, 9153)
(-1514, 25458)
(-1290, 37207)
(10, 4122)
(1788, 30538)
(3312, 164269)
(4963, 327718)

Commentary

Curve 2-7.ec from Layr Labs / Yukon Elliptic Rank Challenge with conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 09:49:42 UTC · history

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