curve #3818

y² + xy = x³ − 44763872594139488311377563867277758494507889870670x + 112749806145185989270052886690781031034754326405805484398918964339945662212

a-invariants: [1, 0, 0, -44763872594139488311377563867277758494507889870670, 112749806145185989270052886690781031034754326405805484398918964339945662212]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 106400892111711919061069655856607364120818038880184026700597478350414364355417311050289714361944235784595678942537290
discriminant (Δ): 248866439701747567903139333850893503877301706936112014372323754590882773756163264247237655500377994309906620910475527740041087457681956238090240000000
Faltings height: 27.4495
naive height: 354.5901
primes of bad reduction: 2, 3, 5, 13, 17, 19, 23, 31, 41, 59, 83, 127, 1523941, 651931663, 1787632489444835156699, 19885661019671018507367577423, 101190345129054936031106110228772777
regulator: 8864932370314101122023584773995.024179128113917721006799280923776681829589366903569485240647072
submitted by: 7fff-zip
submitted at: 2026-10-03 04:59:16 UTC
last updated: 2026-10-03 04:59:16 UTC

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

(2808150237543047831311164, 3031563754323172305646541924308885218)
(3361516410244978362511164, 509658720735118842820389045530485218)
(50329194504273957520270876/9, 164901657949972078025066041741240764886/27)
(4361035489048347427912764, 688398037998408962747909440931413218)
(-4462380628224251029620036, -14954750706620593612398505295643716382)
(9635747903511870280340604, -24001517547273169472700573299532352542)
(699606413526435894221797344/121, 9146111917060325261084582573006441369658/1331)
(29286862410109538051589864, 154666393016846751525085667838875259318)
(-6706932882819490915051236, -10548956225276152518417178661719277982)
(29222445894231113085454876/9, 34529091945939912235577756575355158486/27)
(45091300051144493614792614, -299624869606527299876221220413446289932)
(2720226588866708975465904, 3333257760530654485424695694197639758)
(25819167515057082704373564, 127156597620761248813295830379563208418)
(-1138272856882164745438596, -12736894710910189305473575719407219742)
(-194712611553165128834436, -11020821863262572427576304555035135582)
(4350794527699519146189564, 591084438786907884434983625739714018)
(-121294859726779939854276, 10870954385361547040726916575016976098)
(5490937050413151794042964, 5701586747566052801594992858456767618)
(3208893802964490808595364, -1466039040800179030195547187138949182)
(-2516651943022584863496636, -14472925926823287361348921361262658182)
(-7700470420988207695380036, 914332593773617770424291518048776418)
(3324431530850537440351292, -822483223745438728285523294042909470)
(2971001120322111725042364, -2445580666380725930773126193729809182)
(4707470415746680987979964, 2518740153869562558162670794578936418)
(-736789949075936632385508, 12055347534732485313227116520155067778)
(2500355626308185475842364, 4056584079114516957221067202665166818)
(1409696071802734899642564, -7242082536281927462094821977884024582)
(-533444779558171557653316, 11682339725799237495867054462501629538)

Commentary

T=-10979/174

last edited by 7fff-zip at 2026-10-03 04:59:16 UTC · history