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curve #782

y² + y = x³ − 138457897x + 681816984246

a-invariants: [0, 0, 1, -138457897, 681816984246]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 43407145415402227336531
discriminant (Δ): -30949294681181788090946603
Faltings height: 3.6300
naive height: 68.0192
primes of bad reduction: 23, 31, 992689, 61327955520683
regulator: 4029623.86460364386722928270316373694553626444827884974384970
submitted by: Michael Rubinstein
submitted at: 2026-09-18 12:39:12 UTC
last updated: 2026-09-18 12:39:12 UTC

Witness: 11 independent points log in to add more points →

(16942, 1788560)
(3798, 459063)
(-13717, 10338)
(6684, 234473)
(83553/16, -20358321/64)
(-13004, 532254)
(3395, -500883)
(20507, 2542914)
(39045, -7402723)
(1256, -714070)
(9161, -426886)

Commentary

From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-18 12:39:12 UTC · history

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