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curve #4243

y² = x³ + x² − 112414537633x + 14506038362533488

a-invariants: [0, 1, 0, -112414537633, 14506038362533488]
c-invariants: [5395897806400, -12533249520615772000]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 16935100540754779100
discriminant (Δ): 13350174942485752096524751250000
Faltings height: 5.0152
naive height: 87.9500
primes of bad reduction: 2, 5, 29, 71, 109, 281, 509, 1669
regulator: 210916.90065412228402592858008785644804817794593880612371
submitted by: Michael Rubinstein
submitted at: 2026-10-15 18:11:18 UTC
last updated: 2026-10-15 18:11:18 UTC

Witness: 9 independent points log in to add more points →

(95173, 68332175)
(205223, -8905175)
(-153327, -167742825)
(192203, -160775)
(168223, 18865175)
(143453, 36495775)
(11068223, -36806103575)
(115903, 55080425)
(260873, 54164825)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-10-15 18:11:18 UTC · history

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