curve #442

y² + xy + y = x³ − x² − 13726712801000904290088341272158565293041168623859938751245316012367x + 19558755605299435356266450889897244452377885866483722103879303166884961624067395928673936320669626391

a-invariants: [1, -1, 1, -13726712801000904290088341272158565293041168623859938751245316012367, 19558755605299435356266450889897244452377885866483722103879303166884961624067395928673936320669626391]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 3150820384977430359208293608883424294564091544467622072987831131787324102014590615567915860866268681071007822908615118168781890073198260855955552508555674335232469580770
discriminant (Δ): 271699725687646192733286577518625031822437545106002056586462275802181671252630486164380611220824656488577659302044450835197610654138474077293389412541369981252145070435260693284903863672927060480000000
Faltings height: 37.3816
naive height: 475.3835
primes of bad reduction: 2, 5, 7, 11, 13, 19, 23, 59, 73, 79, 1972787, 1073064856409466957317952926773993823036320076107174190317636026026992026798276605152282326705295670150815506167773981598929405884220131424313683747511
regulator: 285493292614275260510055735.7202500569490653385120306139971534563827162178992
submitted by: Nikita-Shulga
submitted at: 2026-08-30 13:55:06 UTC
last updated: 2026-08-30 13:55:06 UTC

Witness: 19 independent points log in to add more points →

(400232331198243283898694078883931, -118865440414895683153385730718497388137230863080226)
(1971845329445421932408231878199171, 12596778492853876287688914900875291893269637756214)
(74958685327433816443875944382881121, -20498019935913045312839831340630216591464231941406686)
(1530159551025999492410166271768871, 46231942469432020842330267619023281910665087757814)
(3275488670189006573837446235350409, 98687443211296863562461458230595985200232753988514)
(-4220748545056935634351217941545831, 48003254317762281723570990392757797581986291900194)
(-4277636613305617610383155417610709, 1923940175435054653330331092833899245448408136774)
(-764791629782241520308790348951979, 172074109806432344404088445727579458635616420630264)
(5282059744971517147824941842295515, -307284436445631604512076398595621708773018196322618)
(-4213593639848681915711308974748179, 50870808035128808807472176966038443030953710726514)
(2497879582781103243614659365792499, -29263558393675661556532589589474509274888371058234)
(-4268985012002365402360002468171789, 18944897597902759845213480934803254208355866483654)
(-2693993923257735708375941590458479, 192318739080599897699614926944331665408732006647714)
(7351437979641467369684478974922619/4, 185692175300441448163961597338962788780795304952157/8)
(2087839019169086455481333946104071, -793185434311046601923390988482551924748954494986)
(-3089176592755684880510181525503079, 180230258628407305505256726750100203769069228455714)
(2051428818156733880156611312785811, 5703750516052927574070154063762507820244454484934)
(74588885618782482972227082007263220171/35721, 4591341225125944477855823471928242119387525515048927326/6751269)
(6272377700614842351449247830763571, 424537443112017651883535844150707026021302063369414)

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