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curve #778

y² + y = x³ + x² − 2741906470x + 54779656199380

a-invariants: [0, 1, 1, -2741906470, 54779656199380]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 27044058554572306801893
discriminant (Δ): 22889252794774808735611376517
Faltings height: 4.2600
naive height: 76.8094
primes of bad reduction: 3, 43, 3457, 4211, 447641, 32171231
regulator: 2569123.25997041592329768808032393597840673019443882466531178
submitted by: Michael Rubinstein
submitted at: 2026-09-18 12:38:32 UTC
last updated: 2026-09-18 12:38:32 UTC

Witness: 11 independent points log in to add more points →

(26753, 757552)
(32945, -454145)
(-32458, 10468156)
(-20848, 10143076)
(-43294, 9609403)
(80309/4, 22375949/8)
(55391, -8535479)
(-53356, 7013020)
(23657, -1776137)
(40685, 3251380)
(16709, 3691939)

Commentary

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

last edited by Michael Rubinstein at 2026-09-18 12:38:32 UTC · history

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