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curve #1701

y² + xy + y = x³ − x² − 101972053130x + 14694054710403872

a-invariants: [1, -1, 1, -101972053130, 14694054710403872]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/4ℤ
conductor (N): 56379384519975
discriminant (Δ): -25413560164729835479913001965859375
Faltings height: 5.3227
naive height: 87.9756
primes of bad reduction: 3, 5, 11, 23, 31, 53, 617, 977
regulator: 2401.6586852374427058320463864272271917579278132237
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:12:28 UTC
last updated: 2026-09-25 06:12:28 UTC

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

(408090, 202385248)
(-1164411/16, 9436565965/64)
(-291510, -140025227)
(214743, 51844660)
(2492589/16, 3251481865/64)
(226864, -57001920)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:12:28 UTC · history

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