curve #1885

y² + xy = x³ − 22768330899388011079379756031421976525235x + 1223638449233293618785775724478319671074521101106882584109281

a-invariants: [1, 0, 0, -22768330899388011079379756031421976525235, 1223638449233293618785775724478319671074521101106882584109281]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 19907996586218313503567898790139872491486814727391866613750345837281469579901523915683123439390994
discriminant (Δ): 108564310752767500724912898619461482451965137139935759694866682850973699810656483737490124536205783380355198159275389878272
Faltings height: 22.1586
naive height: 290.3922
primes of bad reduction: 2, 3, 11, 13, 17, 19, 31, 37, 67, 84978065769370434955430744743092691232542894027854190000677164904289220936317567324669
regulator: 304331755754179835332652191.1321341170808575623641952214631936289206445137954630827489408
submitted by: Ritik Jain
submitted at: 2026-09-25 17:34:01 UTC
last updated: 2026-09-25 17:34:01 UTC

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

(5138096981301540786639/4, -365858589411552327950621466646167/8)
(57282490653842364116, 327676444344958883376149759033)
(909629693065821657745442713831308702371188344/687681801591878066963929, 27262705584445094880182603126799494650555014133846163369300147806389/570271013664878920457340653985949283)
(12722209839356073922544304/15625, 44644122413561942398750543218655924533/1953125)
(16625713452090069723294/25, -2092395218533209775023827289890763/125)
(4279811803233249710646, -279814562759210765665573697117367)
(641889556429768687002/49, 330354792209030632349384300008359/343)
(1243678516938880458798, 43549394992715728226901900574713)
(19329484686629675261646/289, -10600562864452217880212310440055/4913)
(1147670830657409337375/4, 34232686094535152592037182785397/8)
(364868288764459444326, 6441327411267501027672932720433)
(-68522078575760941536, 1569089477528845651421971263921)
(2100161564027335495836/49, -195994755448073113457180720855697/343)
(147210443827495182170970, 56481692885365056799554944281860849)
(20348299659373950054, -876793538964659564229926190999)
(-601539261147371718098/9, -42234410137147825227481994824589/27)
(480156887330700337419957331917558/1139174117041, -9915759280119021798657415482033376247512257260367/1215864457774317161)
(2829150873997875615000/1849, 86688311258067931853754636485082387/79507)
(5952548805039168387496934841275263989311808/308510528777451165084241, 152452824404466344881107911571609700713558456266453163208145655351/171358236947970909920044995660736039)
(-15096708091948761411013831368222905006891584503330/214905987215785493151761559529, 156777591859324359885452697752043956418216176797753093234222832019420868173/99626018073033761094659289522778941032828917)
(17190137173532839116798235860945909890304532/4137243230002072116322449, 8941994384352759700964544682895147096818795563444999856675927073969/8415241444139169837141955255639796793)
(-5251645308634507163747/144, 2447111354670344863975397157045967/1728)
(777274137861807372561000634494801014519363593851/12035921747158585711862928484, 198507190978055078627502045104187509642789065958633997721901915007941505/1320441098464450307676214474713238790115352)
(-17283090303204332037080363630428032300124540284/180698684647610948013409369, 3860820302739462844457618179245471970882996466379332940641381069538345/2429027808681021067269962780668698538403)
(9462242249282365255566/169, 774787231912644646716013580717805/2197)

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