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curve #1309

y² = x³ − x² − 4238961433x + 106151317379737

a-invariants: [0, -1, 0, -4238961433, 106151317379737]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 16884362913600
discriminant (Δ): 7127042774953777026624000000
Faltings height: 4.2718
naive height: 78.1164
primes of bad reduction: 2, 3, 5, 7, 13, 37, 41, 83, 307
regulator: 746.61960676754291157891185758796990865248239718487
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:29:45 UTC
last updated: 2026-09-24 17:29:45 UTC

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

(12936, -7313047)
(43153, 1893216)
(42567, 1684900)
(-7833, 11784500)
(53767, 5802300)
(40267, 865800)

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 17:29:45 UTC · history

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