curve #577

y² = x³ − 29876981617633937516547720367x + 2134761825618789732113617762670596827303826

a-invariants: [0, 0, 0, -29876981617633937516547720367, 2134761825618789732113617762670596827303826]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 5559315405573619230665818880405552177115392444078214645856264902627320
naive height: 208.4570
Faltings height: 15.3257
discriminant (Δ): -261884405048248085978968888893595981016065881710961554676342810527857188166940444000000
primes of bad reduction: 2, 5, 7, 11, 13, 17, 23, 29, 373, 252641, 129939091709606364242290500222199044977231168526393229
regulator: 68577152366591592658857.856348909917247572425258099703916755413312360574987563719
submitted by: Jason Ma
submitted at: 2026-09-04 17:20:38 UTC
last updated: 2026-09-04 17:20:38 UTC

(894683822552217745/13456, -1037960902627747722091068601/1560896)
(122676570167097, -561945059675115916030)
(-143291239416643, 1863802960211007881890)
(187427919154465702/1681, -30014952773137186294247500/68921)
(282820180815445671210157/2502100441, -56228956634412681745295105482774910/125157566159261)
(93122320766993818/729, -12490115476888574398100150/19683)
(8533746900929995463/76729, -9206117741797678956683669240/21253933)
(516429821687130972617/4596736, -4365397272872180558763554920955/9855401984)
(24397002834607357/361, -4467779973023966567392270/6859)
(-4006132384061664027/113569, 67871043719586570595126289350/38272753)
(-1373800700309520835809/8994001, -47754939913012950123865255856960/26973008999)
(1232696623283267157/10201, -553858045520095868770752710/1030301)
(129527100689867, -661811253838777642600)
(4654402646267118281857/242923396, 4743123569383459753952197832468375/3786204050056)
(947674585810579564587/8814961, -10641240806090443870318355050000/26171619209)
(6338839069264366893847/84254041, -432548633778766096005635559738400/773367842339)
(193884303496687, -1905364212485907822880)
(86119223104541513967/863041, -307454768806669997018192807120/801765089)
(-7296139865688852263/143641, -102157080948239766791536384190/54439939)
(17077175856740521176345/116273089, -1199223348771744496162068586882402/1253772718687)
(292176520711443041479305/2538849769, -60082840196508711131269818053241682/127925023310603)

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