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curve #1352

y² = x³ − x² − 2402302345x + 43733930797321

a-invariants: [0, -1, 0, -2402302345, 43733930797321]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 77883686473803072
discriminant (Δ): 61047215063393982165598113792
Faltings height: 4.2900
naive height: 76.4127
primes of bad reduction: 2, 3, 17, 47, 89, 257, 457, 2857
regulator: 35440.6385547988360079809244718875222981502188270457983
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:37:08 UTC
last updated: 2026-09-24 17:37:08 UTC

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

(-301, 6667608)
(102499, -29569392)
(174069, 69998792)
(7416205, 20195894736)
(38239, -2790108)
(-54785, -3302964)
(41333, 3879672)
(-2527181/49, -1892441088/343)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:37:08 UTC · history

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