curve #5854

y² + xy = x³ − 1003901373562668200762763458090x + 360852808666071999117279026920889092258856100

a-invariants: [1, 0, 0, -1003901373562668200762763458090, 360852808666071999117279026920889092258856100]
c-invariants: [48187265931008073636612645988321, -311776826687486279518227975771758630630620652881]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 111484378256343012150371356488942839597381871322167760114291890
discriminant (Δ): 8499218108283341998944102426046592550444766396886413421185272308435118982665428017920000000
Faltings height: 16.1927
naive height: 218.8579
primes of bad reduction: 2, 3, 5, 11, 13, 23, 29, 53, 89, 887, 733642630031, 12692782403864393193481756414258080127
regulator: 230803469023397877.804075942782564509961842690081955820700439884945741337304848
submitted by: apkorte
submitted at: 2026-10-25 12:27:29 UTC
last updated: 2026-10-25 12:27:29 UTC

Witness: 20 independent points log in to add more points →

(205335996618940, 12781755444195124358950)
(902076754179580, 13759174035494522819110)
(362952800675080, 6655635380387617098310)
(334354545403780, -7910266046267777202890)
(764704278667780, 6351634687983760637110)
(1271798977241980, -33781535768215804637090)
(15747303030696820/49, 2898649125729053990075530/343)
(735972445430530, 4544506081597593963610)
(376251350868580, 6033043234999358052310)
(2932708955852995/4, 34810352424182188856255/8)
(1378027346487550, 39928275021751098814810)
(447316484077780, 1138262634221447087110)
(-1111920011369420, -10117835893176060840890)
(140337114281980, 14924210360068604870110)
(1173733151206660, 28276020825060422288710)
(1881303661949080, -71629003825764439085690)
(376145409284260, -6038128012868613501290)
(7147702008052276/25, -1232378316759230031252466/125)
(97943036032196080/361, 71430793114443162549886990/6859)
(-700898734120970, -26835855784139533606640)

Commentary

Specialization at T = 61/37 of the rank-17 fibration of X1152 given in curve#848. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-25 12:27:30 UTC · history