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curve #1240

y² + xy = x³ − 3437925x + 1159643016

a-invariants: [1, 0, 0, -3437925, 1159643016]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 542770695987
discriminant (Δ): 2019345206245172430417
Faltings height: 2.7834
naive height: 56.7647
primes of bad reduction: 3, 13, 101, 157, 181, 373
regulator: 4691.0174249424446846254694299454111592494893818747
submitted by: Michael Rubinstein
submitted at: 2026-09-24 14:38:01 UTC
last updated: 2026-09-24 14:38:01 UTC

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

(-7953/4, 101337/8)
(-1965, 19116)
(-1911, 28371)
(-1416, 57180)
(11073, 1143723)
(172285/9, 70922468/27)

Commentary

Torsion 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 14:38:01 UTC · history

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