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curve #1612

y² + xy = x³ − x² − 93665006910x + 11089550580006816

a-invariants: [1, -1, 0, -93665006910, 11089550580006816]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/6ℤ
conductor (N): 4149942570
discriminant (Δ): -535249542663296905937257866843900
Faltings height: 5.1206
naive height: 87.4127
primes of bad reduction: 2, 3, 5, 19, 37, 107, 613
regulator: 233.5060123207146792103686572809942817560357950
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:35:03 UTC
last updated: 2026-09-25 01:35:03 UTC

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

(348705, 144147681)
(-298832, 111476496)
(201987, 20177640)
(30063042/169, 16356436812/2197)

Commentary

Torsion Z/6. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:35:03 UTC · history

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