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curve #1307

y² = x³ − x² − 6040506761x + 157443563053065

a-invariants: [0, -1, 0, -6040506761, 157443563053065]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 16028164361280
discriminant (Δ): 3397529648176928454553827840000
Faltings height: 4.5848
naive height: 79.1789
primes of bad reduction: 2, 3, 5, 23, 41, 73, 409, 593
regulator: 1865.4358683716061614207805454065319954601126288738
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:29:25 UTC
last updated: 2026-09-24 17:29:25 UTC

Witness: 6 independent points log in to add more points →

(198893, 82606800)
(-7624, 14249673)
(68621, 8127648)
(-661763/9, 385687000/27)
(-84007, 8487000)
(266168, 131933175)

Commentary

Torsion Z/2+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 17:29:25 UTC · history

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