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curve #1320

y² + xy + y = x³ − 6571364219x + 204874375164626

a-invariants: [1, 0, 1, -6571364219, 204874375164626]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 5998023791070
discriminant (Δ): 28632599339361354397645740900
Faltings height: 4.3841
naive height: 79.4316
primes of bad reduction: 2, 3, 5, 23, 37, 61, 103, 613
regulator: 463.59006949093651536264120164351104884222421323322
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:31:37 UTC
last updated: 2026-09-24 17:31:37 UTC

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

(14523, 10599418)
(-61239, 19463572)
(261527/4, 58917009/8)
(2886657/64, 238404581/512)
(2100597/49, 471526714/343)
(75381, 11703556)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:31:38 UTC · history

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