curve #1978

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y² + xy = x³ − 274299621172185878180425268700x + 122312662174981641173896541924530798681577232

a-invariants

[1, 0, 0, -274299621172185878180425268700, 122312662174981641173896541924530798681577232]

rank (lower bound)

≥ 21

torsion subgroup

trivial

conductor (N)

6618012063164615246497093533393406911639384585491221808975754367971330

discriminant (Δ)

-5142030948396065290562335694955718286175649245827743066205732064391687683557224505548800000

Faltings height

16.0944

naive height

216.5535

primes of bad reduction

2, 3, 5, 7, 11, 17, 19, 29, 107, 12433, 15439, 174991, 403867, 253222491491, 118872604130364898194343155329

regulator

42518672469522141479.137194641230328703239511551719001587278358303553659631398688

submitted by

Ritik Jain

submitted at

2026-09-25 23:05:46 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 23:17:38 UTC

Witness: 21 independent points log in to add more points →

(3829000301887155977534410714218894/51433208814440250625, -3730897237542223628604923595126273475080686366621472/368863285202646852845053109375)
(20263094694108977496/97969, -264544096872784651639762939164/30664297)
(615400282015194, 13659116011633425091638)
(51811217151658794, 11792712003140686214377968)
(-1452477013819475170551/2611456, 42791333228775983456729861339283/4220112896)
(1326947225597628204/10201, 9710705784366298750535727648/1030301)
(-129450935518371777096/2563201, -47863281672535142000951340132252/4103684801)
(74418952086730890696/237169, 946385328509368051553913090684/115501303)
(-544531357721822209416/808201, 819645003940064019236161080972/726572699)
(-5038659155769224/9, 270544466787561198255116/27)
(6258253457215269656/169, 15654413597161435903006181396/2197)
(342206046673104, -8277663181080656378652)
(13613844222510456/49, -2819063770508428237868676/343)
(-588293180778096, -8948716857825675348252)
(6039443414947604, -467711078251844170250152)
(3455770029699684, 201107927913979040769288)
(-146100239836075768/361, 88647628653465790506905372/6859)
(2728541352186200205601013084956/28593779513884209, 47622070205887589305378787101588349718459888976/4835120990551640936715177)
(-8522069531707320193433360890012248618/15549427346521149966361, 20152502425760068081710650708769835607260716169414582578/1938972274987288574525854229462141)
(-14300842151663315732138712/22836347689, 24033410781052040826131977376333232180/3450960353718613)
(-1382006306148344314123138022632/25005540614748409, 46333564068635166688483771753899365549097663340/3954161220183648407187827)

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