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curve #1404

y² + xy = x³ − 409007301453660x − 434297956632538764528

a-invariants: [1, 0, 0, -409007301453660, -434297956632538764528]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/12ℤ
conductor (N): 103961130
discriminant (Δ): 4297500423775659881602671879686795034624000000
Faltings height: 7.4461
naive height: 112.5479
primes of bad reduction: 2, 3, 5, 7, 13, 113, 337
regulator: 33.6395865679016293026011129405233407822697
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:22:04 UTC
last updated: 2026-09-24 23:22:04 UTC

Witness: 2 independent points log in to add more points →

(-95939779656/5041, 7648691913198588/357911)
(-64023704136/57121, 65090420338725852/13651919)

Commentary

Torsion Z/12. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 23:22:05 UTC · history

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