curve #638

y² + xy = x³ − 21601140717124658847409084300971282217672732248838117772491145x + 45527987555658781145734355877692377705631051622938186773616680794156928492236909012836912025

a-invariants: [1, 0, 0, -21601140717124658847409084300971282217672732248838117772491145, 45527987555658781145734355877692377705631051622938186773616680794156928492236909012836912025]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 27066508244510073921658087891166336412955859019867269431485551763871451738266396236719425143003823680626396919356000574684995397266702357977425793424490
discriminant (Δ): -250373850886009576106043684894612915027454808911636465166930682239049233259873861652850605994649857315371186652763094424628944053200117281110284515338993867765861354185169261090406400000
Faltings height: 34.2948
naive height: 435.6251
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 29, 71, 223, 1617889680203, 551020209790232094732344943497, 129524026464566735336202177323150339474682036825956475022638839668905189242290626508588926486713677
regulator: 557751831897813539819081692210064864.1892476288494538245759451055802254759667143139343600128926
submitted by: 7fff-zip
submitted at: 2026-09-08 03:58:42 UTC
last updated: 2026-09-08 03:58:42 UTC

Witness: 28 independent points log in to add more points →

(-430642157341793684272247545910, 7399357111143542063184334673473254941214401155)
(851658033830411724051704235040, 5267725156749171611484017175021311702493970555)
(-1906695838190541455499544507498760/361, 24034103474895616078664105303692544359649793717145/6859)
(184486563972836125282795338582130, 2505017871294920818556006010500604357757005280315)
(27935615831676285811113156407110/9, 78179822509994444813913048961840767711608150185/27)
(-674516567094036037188523305380, 7732491725291259751079291804488632123300808225)
(13648559025208107163465617067126, 47887370938642043995875401957148506099842257727)
(67840874218412554964187192074841454/9025, -15044467326655061195705355214422252247234626789210523/857375)
(1847971094988121500126372879610, -3452610598866944758340713203468209412690985565)
(7370378007215255465697885487240, -16932116459057093783116341386455257733214414645)
(3885800425474544350480298758540, 4501521449945398820100940436159780284760093155)
(1263338206995541224202352616292, 4500528696210290317371032762319411749662856137)
(-5362647011187390076108332760010, -2673643367576540252981870911918666596775713845)
(1309822802753060137499762641210, -4413785193878024621515554603915858320810198045)
(-2621993580028101991621918652270, 9172798177143402784668130106469379593669549715)
(-5466926842567317608795617146470, 477724323203835268439606399319458868334378915)
(5426597102945050716725162737990, -9386665716628034733351314753933740897473933845)
(1004556868820540177100897622330, 4984189630236568259250877341778330199176387555)
(1995521114755699166753742568575610/289, -73790862705715492879291972946809716842643520159885/4913)
(317364188258497125425394951610, -6221296006173877545001346115864358462028774045)
(-5359456869826238859664512811910, -2711921931540598086871354927251925477822209245)
(1874341180828266620301665283146576208274/386319025, -56278440180327872333291577540242541168606514735605432265867/7593100436375)
(33983223800121886090868710453810/9, 113910330627123750716940379176356472902420786185/27)
(328668077800016668705259330991507370/17689, -183123281371873294302388612544929670510952749593912745/2352637)
(-156402702975723133846092024281475680/80089, -203058389874626352892365294390428802177668786342708465/22665187)
(-27915815881372958060171458375918790/5329, 1503286690655107855449395728462334329569488098394635/389017)
(-5357445641993521399606918246102277527235/10651065616, 8245418129613324939810978412459290724909089840873531253471795/1099232575833664)
(-4644941908722743758689400225010, 6756267853880179385601856375820273438909636155)

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