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curve #3470

y² = x³ − 64182095775x + 4034586984761250

a-invariants: [0, 0, 0, -64182095775, 4034586984761250]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 108929272270777788600
discriminant (Δ): 9888780383727478018039320516000000
Faltings height: 5.2253
naive height: 86.2686
primes of bad reduction: 2, 3, 5, 29, 67, 151, 191, 241, 1009, 4441
regulator: 154456.24847197585875071354774039424255797062276100194147
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:43:28 UTC
last updated: 2026-09-27 05:43:28 UTC

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

(-63675, 88674750)
(38550, 40220100)
(9405, 58581450)
(-2324675/9, 1569652550/27)
(54105, 26840250)
(-3317775/16, 5875194825/64)
(461805, -269965350)
(654481, 492313454)
(212655, 1630800)

Commentary

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

last edited by Michael Rubinstein at 2026-09-27 05:43:28 UTC · history

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