curve #544

y² + xy = x³ − 1232908441991872296656133060672512622453470323523821210740x + 16968416538854823140048200290977411749294289869256030393316781076698180441098128595600

a-invariants: [1, 0, 0, -1232908441991872296656133060672512622453470323523821210740, 16968416538854823140048200290977411749294289869256030393316781076698180441098128595600]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 1150456582599428604843156390941225969854828123911101055067517045453481039144073731459608743259908499905902140162141496213509683859651488549172508512130
naive height: 406.0201
Faltings height: 31.7261
discriminant (Δ): -4442210866172403438649481333197917420813264760308938062026871132126381408421609320250506212133388827386373097066007054043838632715519846101772265088016620782984069120000000
primes of bad reduction: 2, 3, 5, 7, 11, 13, 1383377, 27693277039305614698495386708609007950522068890553884256792659645678684309149941625835739407495301258799236044339376131006230735029460589223
regulator: 1778997353552223245720048199810800151.098947937333607110423109004210614940149133391985086435899
submitted by: Mundoamundo
submitted at: 2026-09-02 23:17:13 UTC
last updated: 2026-09-02 23:17:13 UTC

Witness: 28 independent points log in to add more points →

(40844841776099548966989487080, 5895079367914832998538680190494367382224460)
(-37137101072781363543957829920, -3396601072464851066705864418613150564383540)
(18112180662953351716130761032, 761233653885329647722577165726613322749772)
(19955843562803001554841344280, 558406411075630233643769714209635203149260)
(20102274091655910455615211096, -554536461542664363818345615056837854688308)
(15165036910925637634467445680, -1326252084431920378190114584030716392518140)
(2740137902409297183175711080, 3689261622175526401296901222266476140880460)
(573694817527674474163689356496, 433736542943388978804340603916388112081861452)
(-5827155575686445615099290488, -4894374367474874370017899595600062096802484)
(10078678894555730005614487080, -2359262196557071280350512334808537492775540)
(-6234767247412645930440304920, 4940946653029521821166221880820603757216460)
(2373993462163109198240058736680/121, 766197362595316378917946533715120637375956260/1331)
(-1832813047411987211742953880, 4384284482705537363945653431825419222403660)
(-32663802421362405880684768920, 4731817824975179867547000894089891358608460)
(3321225993402975170908840336200, -6052342136910716650018998558930533026571335860)
(-2333810048469647984287870158, -4453434535050073310975036166472886413580778)
(8444864458010345262013736280, 2675616485770363772193712262215846634186460)
(-2725181522190290908286610408, 4506448376646734469859596017740106486592972)
(11013364726774742047686707990805480/502681, -245138355676564509226853823239327792641837909386660/356400829)
(19541569133459177946678054713704565220/1351518169, 73101481647541880142036448727900331748483843219203844020/49685862446947)
(46255121716239597871771757803440/2401, -71219827591260049989469202856025593072199625460/117649)
(8868003371218496401865915880, 2594681726580681121348307547033830732403660)
(-443923278174699813845215253849880/27889, -26576233408638241248487834143786604369801418863020/4657463)
(9062591021169048953399240860334904/196249, -665012014029710961673424575619350958029198573786956/86938307)
(17565358218430382635404148680, 855327721514792928133043173463734935092460)
(-17752759206503267435685718680, 5767232914082795169598027678473796969171020)
(56996190145179581041834405684920/289, 423906042592056097952027084244949807392570778380/4913)
(678984049766720287531184342760, 558752737472782064218175698503129308585322060)

Commentary

Fiber t = -22179/4708 of a rank-17 elliptic fibration of Elkies' K3 surface (arXiv:2608.25406): the 2-neighbor fibration that also carries wgxli's #391 and #390. Found by a Mestre-Nagao sieve over t = a/b and an iterated 'bootstrap' 2-covering point search (fake 2-descent over random cosets of the growing known lattice); 17 points are specializations of the generic sections, 11 were found on the coverings; the basis shown is LLL-reduced. Search run by Claude (Anthropic) with Seth Lupo, 2026-09-03.

last edited by Mundoamundo at 2026-09-02 23:17:13 UTC · history