curve #4137

y² + xy = x³ + x² − 162461054296669537017263x + 25053011057178293122889598714940593

a-invariants: [1, 1, 0, -162461054296669537017263, 25053011057178293122889598714940593]
c-invariants: [7798130606240137776828649, -21645801553460531237723414323034887157]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 25734308834706858971955332769520932743750518603545743588632530
discriminant (Δ): 3281339772590071015333900194249199815035256313792793985424484429276100
Faltings height: 12.1724
naive height: 171.9478
primes of bad reduction: 2, 3, 5, 11, 67, 73, 79, 130276771025255590117471891, 1549197647283167057491160059
regulator: 134056814828337266.24721587610336657889178781641287402674404063391505403104
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 01:06:40 UTC
last updated: 2026-10-11 01:06:40 UTC

(-47871904232155985230032259/228709363459600, 772544309762620419448266711895363791841/3458803722910415144000)
(706247651531/4, -346201745957084771/8)
(-270423712927, 221834580354090347)
(260034811374936056/1042441, -7462163488920259175774677/1064332261)
(-13307477361694884/37249, 1392075730429108973426721/7189057)
(239727109520091923/966289, -3992141882993066894347352/949862087)
(105270196045159/25, -1075308247977912663008/125)
(1619449185211361946/8219689, -620192594727349492357343631/23565848363)
(9379863043965037/11664, -810983675255608692636065/1259712)
(1121878998653163719/5189284, 69769858493230938869216057/11821188952)
(-922594465370894/2209, -14702073150442379726231/103823)
(-158687082174046/32041, -922257805021647164133083/5735339)
(2389421374690786/24649, -391133316521848490045461/3869893)
(7288219936271673/33856, -46558584142835318728977/6229504)
(-257528170436, 223185803755586913)
(134215028129600048066/624450121, -124692806925357573187130028893/15604384073669)
(2607896342529507701/16834609, 4146242490805257614968060996/69072400727)
(-17145612252935384612/58079641, 96250417101477376797192136605/442624944061)

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