curve #3587

y² + xy = x³ − 46538582067849420177295619802498366364593586948210230000088332133930x + 122020162104048395110524763896188225683232675891947197925364672457083229997908236521974767041655897252

a-invariants

[1, 0, 0, -46538582067849420177295619802498366364593586948210230000088332133930, 122020162104048395110524763896188225683232675891947197925364672457083229997908236521974767041655897252]

rank (lower bound)

≥ 31

torsion subgroup

trivial

conductor (N)

2613459269167104381407823252024511182143072084167280276718174240890667915842901387788454347126491442532017033687388050625740201276406405866474083563079976186568515077538529390

discriminant (Δ)

18873293637615744792841945004212471366655273442383806756190880234152157268830943620039928388633798345910644978572443697662276318138255546590960100229668946727171993539749701604154229381431762123776000000

Faltings height

37.7081

naive height

479.0463

primes of bad reduction

2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 33460014957685609, 5859660245116419737613218760297834274263060821, 1262773293588462892087964888381899330245650966170000612891998444079201685351117845538625375566501372113

regulator

319461987093931322480945936746114355208449.3278097623419740115788067450779416528484344809856454866315

submitted by

wgxli

submitted at

2026-09-28 21:55:57 UTC

later contributions

primes of bad reduction recorded · hdeping · 2026-09-29 06:03:21 UTC

Witness: 31 independent points log in to add more points →

(3813111821913591339221118086158694, 2304541619896838359661639817871742469305917672928)
(4061734988932134590156805408594164, 1422759204980708148426127019233925951856550754438)
(4062120606705616642686590969225294, 1779145896181161652554174654150813165535105685528)
(-198793882327254285322742659859836, 362303590065521028524541271515238708605681883472438)
(3804907057116939048517616307571472, 5480063989135491020233438113078917856333485309258)
(3807183538239637081669784948512052, 4797716777719126685639562275823057526990803503750)
(4124212274128430032627944037949684, 15310799408851111588600198260127771263845455248518)
(4214360330521585012463320580352344, 27209520608145533977638711822812355770814521555078)
(4240559954009384741465990285256814, 30426017597717658555408165281582879663883033856888)
(4300981218292284879000040053724724, 37683355793693730017026451238400994981963888927558)
(1620964254919769627442858031446644, 225481503429688628198187663197872673421915474985478)
(1731839010132566481824733596107604, 215909880926165547818280353485575646730073416169638)
(2753194005242422585496119115466764, 121490082445678642674396384536316784181794136457998)
(-1115944199017656090007521787205068, 415409319081496061901236318317990864357274623778630)
(3339007240568585662540603273372514, 62080504240948776592023090579751694993070098689988)
(3459437513886503067051189978419444, 49238025581171877287937182309682181388698613228678)
(3467588588397718087990792033189844, 48356828128256811298989968598010245860733363095078)
(5763660840903216975542609830587494, 212732556101042448233651175930907180862954803745978)
(27257422652061617041125155454064451/4, 2786451064803544366528024372945023602062259888799199/8)
(-6372388826434455597685445690219116, 399770367701986293616572252670118443189560786075398)
(-3080600880736832005005140470258816, 485954466065549476211184772588204943564366779445018)
(3751529834568065498902896992047646594, 7266275989803309705327716882522750786013160051246433828)
(-718869999431193588616974050526762919/1024, 12873498663504467930927483108106903280833062480596364179/32768)
(18418985922487046288868726281265193796/4489, 3625504917956793306525042921633767538998499011660971874/300763)
(1956330482225652397451000612340728893696/514089, 1964510883726948137902433156920682552500608359501958204194/368601813)
(462936914600579975837735889793563397736/113569, 263821914775195463286107703364303639143172997216646413234/38272753)
(2473672659856695191375852575556793850004/606841, 3264262213036544746906889098640949212734211267680038886642/472729139)
(-1091499676880372275526895751812755869564/619369, 217205714467593840491079395657899191911727738859319520786434/487443403)
(6812405553180606462722940067129401027476/946729, 368150522272826287710334144589601557868844806231826152022526/921167317)
(-28041953813744181363582514008537684558316/6661561, 8481329264432613713176388569366291430738819933375717379489998/17193488941)
(206754728967167350900233622792512496243818496796/7724158302169, 91216257627297446494570906984583597509900692751555169910693193861539494/21467266547245265053)

Commentary

Specialization at T = 615941/344779 of the rank-17 fibration of X1152 given by: y^2 - (Lx+B)y = x(x+D)(x+E), where B = pq(L+p+q) - pE - qD, L = 53225T^2 - 5382T - 1649296, p = 23392T^2 - 388744T + 321049, q = 3225T^2 + 41465T + 91436, D = -1945905216T^4 - 372233272T^3 + 123604848143T^2 + 86885579008T - 271295880791, E = 46(32250T^4 + 7567790T^3 + 75049931T^2 + 405133915T - 1687036604).

last edited by wgxli at 2026-10-04 18:07:55 UTC · history