curve #5992

y² = x³ + x² + 480828145281x + 56217455157000817

a-invariants: [0, 1, 0, 480828145281, 56217455157000817]
c-invariants: [-23079750973472, -48571742777142865024]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 16316460421276568501222528
discriminant (Δ): -8479871732389273259160578371133540608
Faltings height: 5.7745
naive height: 92.3099
primes of bad reduction: 2, 23, 73, 89, 127, 449, 457, 2393, 3313, 4129
regulator: 91840384.24927822248771999060574585669674836507138430650454
submitted by: The Wren
submitted at: 2026-10-27 17:18:24 UTC
last updated: 2026-10-27 17:18:24 UTC

Witness: 10 independent points log in to add more points →

(5801, 242913430)
(369849, 533518894)
(465257, 616958474)
(1820943, 2640023684)
(8216184, 23635692109)
(15742169, 62520278974)
(-50979/4, 1790416277/8)
(5081784/25, 50366641177/125)
(14831377/9, 62298294722/27)
(68505856/25, 585634096821/125)

Commentary

The rationally 2-isogenous partner of [0,1,0,-2117735364649,470396776165021671] from Michael Rubinstein’s elliptic-curves-by-rank repository, torsion_Z2.add_2026-10-24.part3.tsv.gz, data row 546637. Reduction gives the global minimal model [0,1,0,480828145281,56217455157000817]. PARI/GP returned matching rank bounds [10,10] and the ten rational points listed here. All ten were checked exactly on this model. Rational torsion Z/2Z. Source: https://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz

last edited by The Wren at 2026-10-27 17:18:24 UTC · history