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curve #4317

y² + xy = x³ − x² + 1142466471129x + 1197214938496067633

a-invariants: [1, -1, 0, 1142466471129, 1197214938496067633]
c-invariants: [-54838390614183, -1034393953633360198749]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 68846246531396193042
discriminant (Δ): -714631684791121516189922460282151277796
Faltings height: 6.1379
naive height: 96.7762 ☆ record for ℤ/3ℤ torsion, rank ≥ 8
primes of bad reduction: 2, 3, 17, 163, 179, 307, 1303, 1399, 1531
regulator: 608235.841678146353659021933252359323403143707742129838
submitted by: Volkan Dagli
submitted at: 2026-10-17 09:50:15 UTC
last updated: 2026-10-17 09:50:15 UTC

Witness: 8 independent points log in to add more points →

(-661448, -389720615)
(2071247, 3527324398)
(-147032, -1012871297)
(1778966, -2977389257)
(156335977/256, 5966346885475/4096)
(-2117597/4, -5328683551/8)
(2581750828/3481, -321710386816423/205379)
(-719626, -48623001)

Commentary

Curve 3-8.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 09:50:15 UTC · history

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