curve #4628

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y² + xy = x³ − 826344048009115658689632423407608657285x − 914103232945117646282088671130255133252545429220298582719

a-invariants: [1, 0, 0, -826344048009115658689632423407608657285, -914103232945117646282088671130255133252545429220298582719]
c-invariants: [39664514304437551617102356323565215549681, 789785193264581646328227840399884107704545716360990152144695]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 1654931758598356861737505042794803450985219219546468670571684358
discriminant (Δ): 35751953894038061234013092875914116987012370734026280566398424690279789460177224342716753518059470093811560385184028672
Faltings height: 21.4379
naive height: 280.4438
primes of bad reduction: 2, 3, 7, 11, 19, 31, 37, 61, 137, 257, 283, 631, 977, 1567, 2927, 3371, 3989, 4597, 5393, 5431, 5443, 69499, 1019273
regulator: 2414615786290217384.56114809455501964086009624533670506043608264493197951
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:31:35 UTC
last updated: 2026-10-19 03:31:35 UTC

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

(-25561847031153615754, 59215377813225175712244737771)
(-26710470987904909208008003657309966/19622422369123249, -39662670324314779848231162849075232259237084791258081/2748710043944859759945193)
(-23659974598320189787/16, 1117012044778440831196630817237/64)
(-4083070704084123694, -48906514543846299659100776089)
(-14367711400940248414, -89401491332633695236782771017)
(-21474343111978344742, -83236137754666977035249586481)
(-6172318552860136027527134350/1034973241, -2053022736778755067286706785470364703793499/33296124136211)
(-97973395617074675054391081103352024680/3673793588988204361, 327021657330442670657652935882304662001101482311157404491/7041612593374412571416727109)
(-85367990933528371539873216748990/27397990707481, 5790637970003877192302616140354522788761236561419/143409549342084165629)
(42171662687446229996, 198085212170615797846755882983)
(51816233238443082038, 308853374278720537498749567659)
(-27824569278220988699931051629139458926/1147887638155603489, 85858255523708477355511064866908630119217800333594340937/1229841286145160582572593487)
(-73176181030779141252064442651/3187731600, 13892810664751824013226716613582363050211123/179979326136000)
(-16871699069170908148224922824798424/1488416014200025, -4803093196808298091119335752519922228574330350124709/57423082385756893499875)
(-8378594765323616072204499328/345327889, 447013296350701521069156635619941477942681/6417228161287)
(167306324910746099628656834/483025, -2156566753983266603483921710754350032863/335702375)
(-94635379246392545600721500422743046058830/4152561018567130277329, -20868404266341082234913092264646929220450320030157474231283823/267592559875783753419622306826983)

Commentary

X400, T=1253/4597

last edited by Andrii Prokhorenkov at 2026-10-19 03:31:36 UTC · history