curve #1853

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y² = x³ − 20286006254473062800149049486117190612x + 35357091311489812541926999132883935786684212120251541284

a-invariants: [0, 0, 0, -20286006254473062800149049486117190612, 35357091311489812541926999132883935786684212120251541284]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 16600646919049182102065685077249599229660578859972185049863800502177145015672760
discriminant (Δ): -5772639382182237855582290093406880993282602072917794149188370238191749871455635663842771497003741329807500000000
Faltings height: 20.2831
naive height: 269.3333
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 29, 37, 67, 73, 157, 197, 1318727, 973818451625445620556084215217476205545468192306976259
regulator: 2261155832244207372655.483074960538843943202478232824335231513102696938471337440103
submitted by: Ritik Jain
submitted at: 2026-09-25 17:11:52 UTC
last updated: 2026-09-25 17:11:52 UTC

Witness: 22 independent points log in to add more points →

(18774424149261309274052382569575619149552408/9729793933880123538359521, -55945560340969557031359270876892313075526398953391437563432828750/30349774160741493674582195343572502319)
(417952833446368907033737/97969, 157731562819761311146768263998611875/30664297)
(24028977545125076806078/121, 3723850095432111125059381833452310/1331)
(1635837323475861283258, 66161984760372470397821549396370)
(2517593130257952448, -492320372655660576748256250)
(2558821035298050913, 450420991275033495930630105)
(9295678296963557926648/3481, -98080940098635573848207710355370/205379)
(95260055452414991590/49, 619966683865451749604976474606/343)
(-769302146275594010, -7106888672985241964292608898)
(51668661215028296872/9, -280735419812144236635089219210/27)
(2841242969761104793, -809945499556163897368429365)
(237753528328100866198, 3665330029162756637327529641250)
(104703058960030746202/49, -455869796213367106679173601250/343)
(2023979932652206945, -1609299519349425792259458087)
(-4764531005452893142, -4883845073169225254523547570)
(5307497889664616698, -8786290308284997058355327250)
(3393580952834659754556425777/325549849, 181674538499891529647050572253110751392575/5873895925507)
(2131719101246018128, 1341655079246584199580135510)
(81053753686275582862312/34969, 5810527053312369513144823965757050/6539203)
(82152020002049649908569944160892704092890968/50805180626375047352712241, 943102394061663395138435173746786974418402898866617242830308681250/362127911221064717402883739197597345961)
(12424508366345809297687893589897349712128/5801163833860370681161, 581847456622334646923757003040134668634295325047941025321250/441847799228677908287719727369659)
(10039940149177434038894922593358752/3667550299451809, 129268022709342586592088094760912584020410151889030/222107957402542286938127)

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