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curve #2029

y² = x³ − x² − 38802409025x + 6511676157345921

a-invariants: [0, -1, 0, -38802409025, 6511676157345921]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 5991327633625214784 ☆ record for ℤ/2ℤ torsion, rank ≥ 9
discriminant (Δ): -14578554460131365748675770618707968
Faltings height: 5.2440
naive height: 86.3479
primes of bad reduction: 2, 3, 31, 41, 97, 113, 233, 241, 353
regulator: 60232003.119067113608989485252304769686563612312090707664
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:04:05 UTC
last updated: 2026-09-26 05:04:05 UTC

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

(144437/4, 574533189/8)
(39891, 70903356)
(-8131037/81, 70661258612/729)
(8119191/121, 86362544976/1331)
(2763296, 4582496079)
(197086799/529, 2545458001992/12167)
(1813971, 2430015804)
(1361568, 1574116977)
(-29197, 87290892)

Commentary

2-isogenous partner of curve#1383 (NDElkies).

last edited by Steps Unbounded at 2026-09-26 21:43:37 UTC · history

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