curve #634

y² + xy = x³ − 357033592821897711084576082253896914177117437475210246668778975x + 2593980489399995178053468512567383693522534199477501730965240507691080747961711695647660735321

a-invariants: [1, 0, 0, -357033592821897711084576082253896914177117437475210246668778975, 2593980489399995178053468512567383693522534199477501730965240507691080747961711695647660735321]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 8131875205055888551538775510894960752079512448510993104277619431720701491735535860670994975070692656410861388413872039270782384933746466742111614102062110627702
discriminant (Δ): 5963427996398181625889345505769868857124292906070753316179625243440200666104859811262173051845377349165011115528006547050579253191337193653622036512067406035889899388180072576802111291392
Faltings height: 34.7503
naive height: 443.7124
primes of bad reduction: 2, 3, 11, 13, 17, 19, 47, 53, 73, 101, 389, 967, 98639, 365112772382318335339, 3425733583687953033512249, 1811857280734145826837546772557191076639962422464599075882616518812052241539410652955252167
regulator: 6822291875004145343808422363887812288.511922393800983030212392650869624256596503796379506150918
submitted by: 7fff-zip
submitted at: 2026-09-07 23:05:06 UTC
last updated: 2026-09-07 23:05:06 UTC

Witness: 28 independent points log in to add more points →

(11795516037323986940691730463078, -4872852365538423550185533868673599740699444851)
(12126393425287196709906931673190, -6901432200708507634714086955985190759453004659)
(-15437283262994692408465361807976, -66533860766447825870686666689092640608806236429)
(11505582078429126858652368890790, 3031822426871982256605514093251530984075942541)
(-1080485529111485517451834442554394/225, -218666949551747543961551066171171826842848038203741/3375)
(11216035016766195786529374339942, 670932985759075882373681871851143816529613069)
(100847599149527709053348597397574/9, -13094070889521380223587155779915753063395837713/27)
(13218222384491585618023912179618, 13569724426389691184231920862906927174661997413)
(470513929388328764852945136356658/49, -2449674679770351092875887482891322192652788950673/343)
(10586385557073410459439081071814, -847321805598192487515775876137652540519803315)
(3710739927125065598859862105150614/169, -160551319949785709155663658373255527224809017278383/2197)
(102155003087019316652452493679772/9, 52639328105924932632166691087432058821249781181/27)
(120506995904106860712128485236381/16, 1166416423454408425174204566077178665550273946137/64)
(74126014795625242033973313470326/9, -393199449424632855209516639950038230514460165505/27)
(15918772459490004808960081608948, -30730723676318516860372121943376207306724379507)
(9066316636939594017336184671906, -10111125777259796986078799684868666822119877639)
(10528035203993396502375691197414, -1428523383573002319533031760643399235992528115)
(465776348882717489447735012976988758/44521, 18308499223854453280793620610006084923291455775421583/9393931)
(-6116268323751592808224461215694, -67445473259203304223126617511201417239544894267)
(13133916108848782067131666870206054/1369, 364188752052566944629260644907248359102974601279849/50653)
(10350419208273754454658274118394, -2717670441538817548039836230799224733917367855)
(955886350693681060580880002310, -47471784909890239054093024837240013342369259219)
(807640056409442982596300311447557398/137641, -1352042990917084753726356867903025829625025088859415697/51064811)
(90655138880882408006571658211213076/7225, 5812104151329108045092132835647290576930255386056019/614125)
(40907740800057808313342345505381290247/3364, 261642156068651543264688779540273421786389751535178772741/195112)
(21754152271155982230997465880284925334/237169, 99462171328414271619170492376465792007939732905812374443/115501303)
(-13997321259510629148150955379610, -69635258214607424308476937258184823899935414131)
(1746155665947023855596661226325701020124/166848889, -4144036545639384926829256670803117560665189297096495221671/2155187099213)

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