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curve #1611

y² + xy = x³ − 5974195981x + 130873262800401

a-invariants: [1, 0, 0, -5974195981, 130873262800401]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/6ℤ
conductor (N): 3913593970
discriminant (Δ): 6247137967466685101508153835520
Faltings height: 4.6177
naive height: 79.1457
primes of bad reduction: 2, 5, 11, 13, 17, 19, 37, 229
regulator: 138.7991809553130272497083841526626137924119550
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:34:01 UTC
last updated: 2026-09-25 01:34:01 UTC

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

(-59902, 16576767)
(-1881934/25, 1556032899/125)
(2575874, 4131023103)
(546210, 399510591)

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 01:34:01 UTC · history

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