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curve #1666

y² = x³ + x² − 3062567177225x − 1749132073151094000

a-invariants: [0, 1, 0, -3062567177225, -1749132073151094000]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 16804238845740
discriminant (Δ): 516700119781167020124426514790061426000
Faltings height: 6.1503
naive height: 97.8644
primes of bad reduction: 2, 3, 5, 19, 61, 109, 241, 9199
regulator: 4962.60251647692442826517235788955081524433517267
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:46:19 UTC
last updated: 2026-09-25 02:46:19 UTC

Witness: 5 independent points log in to add more points →

(-384578315/529, 3712453159155/12167)
(-5228555/4, 1150368015/8)
(2413549, 2217807195)
(-24263151/25, 69485992857/125)
(2924438635/289, 155629501708395/4913)

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 02:46:19 UTC · history

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