curve #4131

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y² + y = x³ − 8583077787883825816952218907397476249367x + 99585150201960344612909139522472149110077785367691133357996

a-invariants: [0, 0, 1, -8583077787883825816952218907397476249367, 99585150201960344612909139522472149110077785367691133357996]
c-invariants: [411987733818423639213706507555078859969616, -86041569774493737745553496547415936831107206557685139221308760]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 445331725536250152394654304235936781427804499173046905275224582251284236014167706659647559277136729379831739529
discriminant (Δ): 36183524377621626658246991906997405147932254648117362218102225476715015493047178987898418774467794594116471958731159201157
Faltings height: 22.0169
naive height: 287.4654
primes of bad reduction: 3, 11, 19, 31, 59, 113, 51770293, 56959501513, 129489523709508185186979510822567047795494195018553571606916229694143561701211668571
regulator: 564554545448758650550600811392.198175504417082601009945519126739966514463182089940573041833
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 00:37:24 UTC
last updated: 2026-10-11 00:37:24 UTC

Witness: 26 independent points log in to add more points →

(194182594257395161704149/1681, 55546449752907208815998248212144101/68921)
(-3505525566343651720401287587/69272329, 366616992591157062734560855291125634749343/576553594267)
(180720900956061581657, 2109691016239464685653760439629)
(104286426244353951061331081/693889, -858184544063725201459403685432971521678/578009537)
(-121025473215106441459182/2209, -66103260453148326883151064725910365/103823)
(668363366739328974497/4, 14599723931046107361724085574203/8)
(573583489664794923537, -13560394744429097322465499473171)
(559200634229791728657/4, -10219778794051464243002896954061/8)
(1981462065151976702604/169, 52153076297938324067475568905240/2197)
(-5735355573921470024802295/58564, -421915172629787209785172148002553839/14172488)
(4416309211240584587070/2401, 34058111932003805382136369439902958/117649)
(9970762858763983086, -122460489373495388008339291266)
(725405585001233106470, 19380180914729721095905214080822)
(1265876845958097186407361/8836, -1117544053504126844945994189791642955/830584)
(4898457346017670344155/49, 168246099654150376402838957126386/343)
(1187136498214088802444169/12996, 413134706881946122398151525680594769/1481544)
(687459358064352157837/81, 120562151432597827509911720317541/729)
(11788336727558953220, -6565356908306319447084176273)
(-3803307648792129929607/121, 774175568283161494285274677948023/1331)
(232532274284518037865209/2500, 40685555962693839782249425785757823/125000)
(11640692613174313562, 35349122826999591950310028954)
(105495229214320351935105/64, 34211100058694760917937423319881409/512)
(64471636191375237559593/676, 6772824184553010924369772670826183/17576)
(37350090738530662577/4, 1138549224212556134542875561653/8)
(225868693460788801018370/121, 107214087304495707752071730372805782/1331)
(41720597226809337281289/484, 158662283371029774600711752571327/10648)

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