curve #5503

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y² = x³ + 12881993947854714618575473225

a-invariants: [0, 0, 0, 0, 12881993947854714618575473225]
c-invariants: [0, -11130042770946473430449208866400]
rank (lower bound): ≥ 13
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 13509068122816118157587695955324550113332646320712100
discriminant (Δ): -71688571807348294226870626126120790086422354230122901070000
Faltings height: 9.9722
naive height: 142.9744
primes of bad reduction: 2, 3, 5, 7, 19, 15643, 23173, 80359549469599
regulator: 7690373615256523656971.670993372490465673094740035942480935428236
submitted by: jesper-petersen
submitted at: 2026-10-22 15:29:24 UTC
last updated: 2026-10-22 15:29:24 UTC

Witness: 13 independent points log in to add more points →

(70058591443126834636173328801017979458716459/18767646959406019746086878727896249, -654994266033656109974243114268578211066038227799072405218441721598/2571074955169089006826142986318569199804372446255443)
(1053388361983201848698980262278281539261519/192670556105239374337654762391641, -1122944418334418197547500920362089648282333430459331947089004328/2674379449163031407276040167089986747343006084189)
(-2689547490026102813674788184165751266189/1566256156091626859880090126001, 173323015344254728122243855356264706808449551819409351540366/1960172023590078300213576219370198682588689001)
(-7179416192517440189775877565612817015671701/15984631669049704845577518139737529, -228566604409263250787449138017653860241035903391666051878160805618/2020942467045762391003078027190313050457174744719917)
(25755022952779779424675867327799831399/1287538649868707181441924289, -130810353429022083651445182006159360145056719943923391168/46199833681888729911057254899566316285663)
(3113104299792992121563573274555727148248667760042991/493656436524953039154399666760870749985209, 178101463924745269980295715095367414726222075582319086429805358077414166433464/346846411715623898902651589415382326920750423654208258958313427)
(14259510003278210406188386992875043414794873744236457339/4100706146328346471140352023128527801527738025, 61544590268808914504497927678457129969505196695620914316457582544112429273964776562/262595919795024733671569151505302728370226852265602018326517448928875)
(19042172535695015411929220081347122524723087643377779/23699626881493214887018788308694021949320081, 13355989716513045441532894266619773811100308361704561834143377854481452517645942/115375145846478037007245147939219029714435782106334182351084179271)
(364720959981064812077981424128365887682885679381392899199/178800422642504719348552184080850135622938810649, -11052214022505337822178935295726521417931917600070868792197468489555673727044234491068/75605399324574720845892842758387819065559108364240389913478702200816643)
(-7039604365931719471456161857126583911611917582214748609/9592736347552241433982599478371408190188219225, 104987895494103145795576239993242010973961396450723900248998810771930338913258914564/939536728656543211817557139416347468706426853112796059604822922044125)
(-1035979264312006142017175916041/451460567675508522849, 271055480994164073129824950963021935733135348/9592454215520181993302330190993)
(-254361930221166725878957321/119317484853224161, 2329207129749261244667046380906597816508/41215078859788191749548591)
(-26524085375632255948446162015570385891943762144991682428679688611457833278152317201102917980321447693700341/48580703669036733177719856717090808300409495510307968897563520722121161759894460559378626479368441, 38187945442781157907415752862648054108596613942744106245763753076948015949788303487142658926004541490661091360548049969035395789072554688622698778506389834962102/338606820361852890769402649036686785363714031289552217192658156954613887238500300610555560647461293561054672052227432529074978702124273068231054989)

Commentary

Found using Mestre cube-completion sextuple (-34,-33,-10,14,25,38), applying the rational 3-isogeny.

last edited by jesper-petersen at 2026-10-22 15:29:24 UTC · history