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curve #1684

y² = x³ − x² − 12528422340x + 539310754124100

a-invariants: [0, -1, 0, -12528422340, 539310754124100]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 6234348120
discriminant (Δ): 206725725871834397618950560000
Faltings height: 4.5469
naive height: 81.3674
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 43, 71
regulator: 39.18302811459079632071885994926347000964409477
submitted by: Michael Rubinstein
submitted at: 2026-09-25 04:48:34 UTC
last updated: 2026-09-25 04:48:34 UTC

Witness: 4 independent points log in to add more points →

(107457, 20828808)
(1191785/16, 281716435/64)
(-108715, 24827990)
(4118845/36, 5306617745/216)

Commentary

Torsion Z/4+Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 04:48:34 UTC · history

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