curve #1880

y² + xy + y = x³ + x² − 471491996692609251251342090472984259170x + 3741029700369396821353217943292940658798826633865187523695

a-invariants

[1, 1, 1, -471491996692609251251342090472984259170, 3741029700369396821353217943292940658798826633865187523695]

rank (lower bound)

≥ 25

torsion subgroup

trivial

conductor (N)

117528433039172922383609959559364712536359007360530440501520225478358133697633113495809894145670

discriminant (Δ)

662181858382197169082695671015177274625145256613188797802697431483726639425101870649300279576722933159192441472000000

Faltings height

21.1701

naive height

278.7605

primes of bad reduction

2, 3, 5, 7, 11, 13, 47, 67, 73, 2011, 104161, 271043623, 27261076573615269739066367515083793671112316300494039466755623098639

regulator

161259286889680341763144828.1315638826227033460480798586794834634018986141086757316315841

submitted by

Ritik Jain

submitted at

2026-09-25 17:33:48 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:41:59 UTC

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

(8732524273774676389574897/218089, 22558596178389338814599227693076447169/101847563)
(8279839516727365673, -20119199281044399246203441037)
(90886955611624121905/9, -83225782889445197151350661407/27)
(152587469301151146217/9, -672643654077890747386275674479/27)
(-19250725904328444167, 75388711104750367044928426403)
(-2762670960719586090481055126242026164127/117967282004823787561, -56416976727160888460987349144736318703986577799180710509983/1281275022317951638438979702059)
(114560235692183759473, -1205496073022891713987219335037)
(-10510556313944809127, -86807562285948247649690623837)
(6547281667508453827/9, -1573990168278851362943204614259/27)
(18090737521145427133, -33645712374563409578048830237)
(9850760601470594073, -7236569904071415983970479037)
(-17484435299572949427, 81484436341401009371445880463)
(47194648687901660420857/2209, 6071365717037138834570207606862349/103823)
(-97834816348189999293/4, -202579567543927337731277889771/8)
(4285227858952838793, -42417796526359563725054878237)
(6216751807912214296785/2209, -5124700869870600782942928392994003/103823)
(40777492621130140777390571233/58049161, -8230487160169671036499685898536865748602383/442276557659)
(438081235916262175894823823073089/49309031717521, 5511515158528465596204403944345501899725270260685/346249943772669445319)
(-20697416210901700530243431/1890625, 226489139198625750904256194224245947997/2599609375)
(-913899975590744219012731251800449268943/37346935123771937689, 5708360134577903936992222773372793966997462079818337509801/228235108415895388930827736387)
(20693816117298137427096009/2247001, 45179965105526667020159737614497813505/3368254499)
(71917756068357909291444659378512289227/7081859097432292644, 8822273642986717659510625573312283614357733554281803339/18846075320915562336450016728)
(-69324036011504093104681966042427/85684662073201, 50922158639907829079123621861989517363417268498463/793148728631454449801)
(28202886058718322200752073215423647997/5579221704123038689, 508146251400622758898833332230261976789019268708681038419/13178331538721461379764364113)
(-80559033887924453391137453649161385657453/6846538339396193151169, 49580857538803205050794183665352934139974936106840094147100489/566508677693516631505768229678303)

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