curve #4255

y² + xy + y = x³ − 6466344494082069296420815388x + 483614503777528795376356363963062024936638

a-invariants: [1, 0, 1, -6466344494082069296420815388, 483614503777528795376356363963062024936638]
c-invariants: [310384535715939326228199138601, -417842931263785344781975472373074931843963349]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 3596232705771186622110065084714548320296938776703770
discriminant (Δ): -83733053232853046027851550426416688235135495410226327301019144348918843739630394312500
Faltings height: 15.1743
naive height: 205.4874
primes of bad reduction: 2, 3, 5, 11, 29, 53, 71, 137, 199, 277, 281, 397, 829, 1249, 5581, 1031299, 6764341, 10464199
regulator: 179065725606537430.70549582803061395052417423461483696558444067265647
submitted by: The Wren
submitted at: 2026-10-15 20:22:03 UTC
last updated: 2026-10-15 20:22:03 UTC

Witness: 15 independent points log in to add more points →

(-75583386525546, 735232175588467328710)
(-48978084270876, 826336794660031435330)
(607710310443783/4, 13874843620904055218681/8)
(182928783735414, 2328533539351317776515)
(948821092025991/4, 28053019023250210488905/8)
(9747367903990791/4, 961837508054298730122905/8)
(-1798545767911366266/19321, 1418349341398934164689435865/2685619)
(4736730945570081/64, 328016932804751885652245/512)
(15543399034207791/1369, 32499349701793895487937945/50653)
(181804091681187621/4624, 169371642655608936702319445/314432)
(127164935038711599/625, 43049227289315700583718707/15625)
(12536267217238829799/116281, 40428450734940197865810167585/39651821)
(27651798649758347319/591361, 242129091355035982903243070365/454756609)
(226677552444616050961/4397409, 4942346945416508368868187935105/9221366673)
(5142675879120738256866/175483009, 1313528777978583577234405380539090/2324623420223)

Commentary

Found by specializing the family associated with curve#802 at T = 246/277. The original PARI/GP computation returned rank bounds [15,15]. Fifteen rational points are supplied.

last edited by The Wren at 2026-10-15 20:22:04 UTC · history