curve #4666

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y² + xy = x³ − x² − 234732158095893260385981576389229x + 1384223546360652556335726475269665692390758688785

a-invariants: [1, -1, 0, -234732158095893260385981576389229, 1384223546360652556335726475269665692390758688785]
c-invariants: [11267143588602876498527115666683001, -1195969144055603757971921525920046914853595007036749]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 4834182615430193767926697907961349712388368645771199790890 ☆ record for ℤ/2ℤ torsion, rank ≥ 17
discriminant (Δ): 2929407914172985561104512836705388423507352432727570955526028994419301020344004953303921082500 ☆ record for ℤ/2ℤ torsion, rank ≥ 17
Faltings height: 17.1848
naive height: 235.2216
primes of bad reduction: 2, 3, 5, 11, 53, 83, 101, 137, 251, 463, 467, 619, 647, 727, 907, 1277, 4447, 10039, 10987, 14011, 16553
regulator: 16163510083800210104512088282.0850158341502046720517093296847773599165510
submitted by: jesper-petersen
submitted at: 2026-10-20 19:13:08 UTC
last updated: 2026-10-20 19:13:08 UTC

Witness: 17 independent points log in to add more points →

(17558214562870001948335020079/7700238001, -2326541210488424331967258788173760423357141/675703584825751)
(175278501933334851010778871759/12498862249129, -40747082919947009143913054316757286872073916/44188140126289940117)
(7907257535364300348658633959/806635700641, -114977680689872596798768914697217597148492/724462915181000689)
(51228413052148977232730917748335/5699319424982569, -10023575510137622851367202116118782784946145340/430263491680567791927253)
(895631212942816881816456323420952967637778067445239/99644428182414440255028083576145009, -731519448510127177675593891267157400188864976017723001284698977949529959404/31454264097452004891077792432649456571702319404222473)
(1742184980273171123828675001/83017744384, 57109052821980638505044639739264268799763/23919736653873152)
(15772411058725366526191711999/648364754521, 1656686084615603486209321694846254882271644/522070432352608931)
(2390794115520384215291415495735/251906956466929, -425263527615146640718344444416571978283903980/3998160656400511577033)
(8863519316128170615337133598615/954759262874041, -2121465037022109156712155836826959867986028100/29501277365453047312339)
(131611899499417132743645685065260028958343636281/14846034005071521042164451804736, -158788769534157689854702108498929600434487152077774931556057134919457/57202587811390837271356532013445108498772329984)
(65949491832351386899915644047836509977210371252239/7447087028594337200202230667556009, 351914060417662239668294183731334146971330275481690483215664124401257721/642657593931401183244279704880578452883473353997973)
(101830878717286489023593245471/11472128024809, 185385158174375882391731198395769348620164/38856705642813397877)
(191544755848832474807145182537691125499031/19167421032716533758647761, 16023923636415701433706208903808925776876650249031358882376532/83916144870552777089088342532116777241)
(5976791658798236446177680477144050241/118655616020182866496, -14002262068822077200143421420323509076005633073524367587/1292505642098942490635272492544)
(49381913497512757791536801320804934197689/483290958166899757830400, -10856806192973602002096408324072788381522745067969829880025173/335979674551181901204910417582592000)
(119733454263475866805463037042811320391/13024299025552276979521, 84662400337459813617164951558512441226446040825611368588/1486385766739326023173519361772319)
(91918540260155189451522101142375983528374195192599/4553628592773479085669929416556161, 678179661874792035404382658008631457994508786260438684101538339971072749707/307281495698508799973151750513072555654334611286591)

Commentary

2-isogenous to ICARM curve #4579

last edited by jesper-petersen at 2026-10-20 19:13:08 UTC · history