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curve #4246

y² = x³ + x² − 52643110305x + 1180828345377919

a-invariants: [0, 1, 0, -52643110305, 1180828345377919]
c-invariants: [2526869294656, -1020250851622289920]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 24713621597826872896
discriminant (Δ): 8734561091179281738162603631542272
Faltings height: 5.2037
naive height: 85.6740
primes of bad reduction: 2, 23, 73, 79, 97, 593, 809, 857
regulator: 454603.52481986601977137192179311135324963007672724711457
submitted by: Michael Rubinstein
submitted at: 2026-10-15 18:11:49 UTC
last updated: 2026-10-15 18:11:49 UTC

Witness: 9 independent points log in to add more points →

(776475, 654562888)
(-114805, 75573688)
(453386, 265538879)
(415467, 225885944)
(-240395/9, 1368209924/27)
(227675, 31576888)
(1146699, 1203591368)
(-40637675/324, -444553398559/5832)
(5107/9, 915995240/27)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-10-15 18:11:49 UTC · history

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