curve #387

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y² + xy + y = x³ − x² − 100866462025735601489061531221367632x + 12314457652529668478336154151601632727445624755257139

a-invariants: [1, -1, 1, -100866462025735601489061531221367632, 12314457652529668478336154151601632727445624755257139]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 132526659334603548941640593425440810800209313878084191942534834840471013814279610
naive height: 253.4109
Faltings height: 18.8999
discriminant (Δ): 167048582015311555617604663872299990347906773432291880826238346789303156222832771470762174681366732800000
primes of bad reduction: 2, 3, 5, 7, 23, 41, 43, 67, 17687009, 8625383858083939, 4347074972399559839, 116755619159694439918706907581
regulator: 31252989195547345853956551.548307535576264872008238291927449484246790498144645440
submitted by: y011d4
submitted at: 2026-08-27 04:15:53 UTC
last updated: 2026-08-28 17:12:04 UTC

Witness: 21 independent points

(148679383908825516101034651687/2892792074041, -419396527457591993040091435482660459748481939/4920121508162487661)
(14915665595629591025943303049/142430005201, -2894645422710853689692401653297154595358513/53752941532852199)
(28804871982149535303767989/175801081, -31820224318598755021172431054138152157/2330946532979)
(41503265424742079667600099/235960321, -13853780526757288419327815051970075773/3624586490881)
(5599802288056289046405325209621/553305384025, -13244869359115280813529010857629721766528233491/411573443380076125)
(6238900184895507343309/18225, -329190034457907265259171971161593/2460375)
(46733187381042083435869751253/306635740009, -3727152705737554232383183995817514500853237/169798621122763723)
(34434268272798885623889/193600, -75534532472778780724922600278843/85184000)
(397779127939378385589/25, -7931897944695755904330185267923/125)
(1011652767689780553096258909/32365809025, -558264632432317893127294452333064713771887/5822770872642625)
(5686371317213161718877/49729, -529029625822318944323219434888049/11089567)
(99026815359625777856187/564001, -1755147899872885162072255832769899/423564751)
(31155217863055516381189509/687241, -173894385302024729747915575552915888907/569722789)
(4045519203287723024859/22801, -6426891351451212989143113319073/3442951)
(1665278338488298509701583/942841, -2116382204558850462441265655070576157/915498611)
(4580746394847860757/16, -5317492422450796456135806281/64)
(282883013563400037, -80113292076764448415868639)
(118515294540874554570017054397/960868497121, -39399758132570387595904638681689958606572321/941880774749391919)
(121457558464369639310997/10201, 42313977146675124353651514907182701/1030301)
(1097329661886908567845593/4133089, -547743617286874176847956014648071363/8402569937)
(1232328788523622159368584301/16851025, -43259929033874283526431992572489338024791/69173457625)

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