curve #285

y² = x³ − x² − 108391804584990603814796450120x + 13755098120758219348428060610562384253731136

a-invariants: [0, -1, 0, -108391804584990603814796450120, 13755098120758219348428060610562384253731136]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 1746512979501225597635228204059275382729246622846831247192424343764785450672 ★ record for rank ≥ 21
naive height: 212.1831 ★ record for rank ≥ 21
Faltings height: 15.4685 ★ record for rank ≥ 21
discriminant (Δ): -233380186227384058848703372008258431165712778081959663733431061992386884073488788139008 ★ record for rank ≥ 21
primes of bad reduction: 2, 3, 7, 17, 59, 5182408071918843462574265904842838694420448840522572897950269262939709
regulator: 1727154497244706358924.4938177747627353663328127637315442353819540947403787820251
submitted by: 7fff-zip
submitted at: 2026-08-22 18:12:14 UTC
last updated: 2026-08-22 18:12:14 UTC

(-358061774563594, 2580618548794289688114)
(1270936304855067291206/7295401, -7864000916274319818672530939814/19704878101)
(18084643464158617/64, -1221223571802293490760931/512)
(44671105442366053028384/256608361, -1651918743741252533095927949054568/4110609334859)
(60121778501938487064/225625, -208716596957929431483331129512/107171875)
(8206392811668797324/2486929, -14355103965797424629815600224612/3921887033)
(846472443530122828/4489, -43539221175942111467537620/300763)
(110271074117235741785/16384, 1156596855050453611112189753763/2097152)
(698386490962371230/3721, -34350254488959727671467814/226981)
(4133176829822336685/5476, -7709234604883511151711473319/405224)
(-295686649431912, -4466883483347542515048)
(525703387509253230729/2961841, -1675321878060206077916932302372/5097328361)
(5248778229601525646/24649, 2221745809770755632335040314/3869893)
(12695230616074388380/116281, 71180725628947167369395630476/39651821)
(-193996925847867/4, 34777407506092937774235/8)
(20366732029320853261/88804, 25919667425597575705778700841/26463592)
(11726549809860429720798/39551521, 689373841952274405977002281313362/248739515569)
(136278393037478124/625, 10909236230990917809316068/15625)
(9181636199062029694/46225, 2473634932553173712167818722/9938375)
(23135768629954700/121, 189981973894104235310964/1331)
(371238920861328542933531864/1863123991369, 665271333093057930708694140777111880392/2543095312631004347)

No commentary yet.