curve #1884

y² + xy = x³ − 21747218184934248435831526041055537013460x + 1221512960793768893176392616007880330398661089355069932598672

a-invariants

[1, 0, 0, -21747218184934248435831526041055537013460, 1221512960793768893176392616007880330398661089355069932598672]

rank (lower bound)

≥ 25

torsion subgroup

trivial

conductor (N)

2609466480344009345395122684864321229758599903569676462528238296630351551849827984029882115796687470

discriminant (Δ)

13665795032532616630862215986298548051143608491687493048735273041205742065258056476541408270032996360298023352231936000000

Faltings height

22.0549

naive height

290.2545

primes of bad reduction

2, 3, 5, 7, 13, 23, 61, 89, 1571, 2029, 3011, 4556347, 593068316821, 132022248515387, 4855982365272817, 460390834656870047746987593322921

regulator

995563643789585912492220576.0039366243091244945754764355092909757493678367007941636169480

submitted by

Ritik Jain

submitted at

2026-09-25 17:33:58 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:42:58 UTC

Witness: 25 independent points log in to add more points →

(72137659084850452631050016729472006386568636026376/1412556163465306332717533689, -612690658578160453452925533724094480367776014482740318473181547679816772004/53089494075176058191549277221632408794637)
(-1982694267520109184891/16, 90815328259711524757199240761767/64)
(-210806529224587193604332/6561, -730047262649420364047513864310163184/531441)
(-169635774402853309416, -170674864930887638267785724292)
(-4605189997400116338745522/38809, -11161253854497004060454111664819489176/7645373)
(126721940995735929674504, 45110478167856853541790313728648428)
(1233115958093220470634024/5041, 1161920988805039357615090493289852468/357911)
(-164744544328386597888, -577023021311171504716966925460)
(54287156810611868699909186/543169, -86174960050586062701281105842728503336/400315553)
(-12334822921078563087174/529, 15937937528482900602203955280979106/12167)
(277012475927360454024, 4056361316668713298157497823628)
(53800449876133512604404, -12478926623037563246157021449709732)
(708855512890881868584, 18492940763305042363562693385708)
(19122737561358823304, 901465140779923058865135161228)
(67029434324634673979112/961, 6247944144218699738737935041121108/29791)
(216636127692828234617094/6241, 351565870459327141516441631298936312/493039)
(-41554835569166184106906919809128/391286529841, 373875308098414586045888175749450639944857370332/244761071724910889)
(-7830813452070597742704/1369, 58760143806029845695933507045227124/50653)
(1002876682012836107109550767871134289131/8618380651008611044, 13063087024174632734193299867155396817316722368051611375609/25301047834874657671570827928)
(91032710584185722434599420451323294485856/826541227839365222209, 9573701311943735827730174610411521001481795018169421005086284/23762754518974887281826698113823)
(-26827270655087757312929965381186135987334484/325538222812460819988649, 290965849376345997430628283378174739255799946958904534924511492744/185738948396166781373012122061985643)
(-1436969008899049001799139456772784/8623014631009, 11818599007050753443414486074416272411299594649604/25321456594914035473)
(-133655312016209129401258826828886/831559786201, 569839940028837366271566366064351749930420622152/758298537476905699)
(516257524591827376700613842339293296/5334179439908089, 59483975193183744017080659618234453487800310625697324/389584286455485717192563)
(28783720918370771412, 787016193679057040148396549840)

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