curve #1678

y² + xy + y = x³ − x² − 8536804896831126925862197870300669864549375757x + 331169743738868005440284545835605051995697843154401112024563827868981

a-invariants

[1, -1, 1, -8536804896831126925862197870300669864549375757, 331169743738868005440284545835605051995697843154401112024563827868981]

rank (lower bound)

≥ 27

torsion subgroup

trivial

conductor (N)

374397028418339688231942221099863406293601350452144111419388010536632037624951844651049337512585958571192803164430

discriminant (Δ)

-7562137013081322919361461802915070366070411245482966617956553014627847894892053419940174241467235010019744904222710138974016873370880000000

Faltings height

25.3860

naive height

329.0696

primes of bad reduction

2, 3, 5, 7, 11, 31, 37, 67, 79, 101, 3094313744047721462887770916861087408349, 28473976775092410201872760927413327649988659077481445248963169

regulator

1782742052163014123540799490740.8012172067988898643704426397883248237311414891473650280636005

submitted by

Ritik Jain

submitted at

2026-09-25 04:08:35 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 05:28:24 UTC

Witness: 27 independent points log in to add more points →

(1548477446150838067114973506498559/4431025, 60933666470845038267377405166056975101251543467288/9327307625)
(-54062182344198893337911, 25192845193144795270868542523925164)
(6168953586916335070877311/3025, 2947087487975665658444776026751603902344/166375)
(40462817071128367871803418359/52441, -8083634765196453931911669094385113472602984/12008989)
(101098071024061162212101, 22392418776950085463412341951351214)
(30174106281982673886991, -10052467651400007973843882526751496)
(59209971762629482424195179/1369, -331586539182379495892574466864445782888/50653)
(36567984256073126016630991, 221131263372362373507860991543316376504)
(8740133848265720184323791, 25837647258703214838315791891743318904)
(26707547149337764953275135359/499849, -1855848940183511962212246473111729448194528/353393243)
(95160357990545128932941, -19507136106196181580209759721723796)
(4192107406705402889020991, -8581121857315790448936737183816103496)
(-795322541552211184188067841/97969, 613237950226892474987082719207017508710328/30664297)
(638215587419466123332193799/7225, -10022580456925769295200909646576878725288/614125)
(152824901246557851392367331/5041, -3583187054809687006613620665800328827156/357911)
(-786508739182435943657385431/7569, -6460010744257064731791998222979312704908/658503)
(232011760106485089115631, -104113388371219733436134929752878056)
(1558834706661956078902737018428615203097940242862685279/40034270742973733355036803302969, 1925838456513564724338865695478913285472667492409775207867822357273055425100816312/253307403256563407465410740680131541818115369453)
(-4976987222232896328442827901/46225, 14609291907788946081415492075319040494252/9938375)
(27035251074205715380021, 10960623831608419177419072893190284)
(-125826877058712843936913910362480508806961/1210320125570832004, 12981546307585969225869006694570459532045012580862812495212357/1331528242126826011598246008)
(-14999260953157718572948820657718088417441723540025381/140229067420064541529184306209, 237934660482233752837746052580930178000793470312115795615098243244167047825708/52511819760033327208413310280966615258464177)
(-26532933788393541611707034712336555398369/606699493552270561, 11774976060003122466698728490603651590434020973193236979619896/472563798355519920731673809)
(-282292455599895812093508939295415688619340178023935023041/14210408442357682581257904768105924, 37609378415994929910616735316240684283532730772528298259730140768565721792039190619703/1693986095332029426976105452167869801696714603177032)
(-2890405839583431643007605564862822741631081601/26865148010515136212489, 9067016964256364960532871921320991909406836815350554015001875061152/4403356587478433907416749461204763)
(-628533527475351550689614574325663021/6610622058769, 286088993529133059375966101044277154087610889377134788/16996656313387739897)
(9622669208999419713200839726738353408383605270591/190844288608659323210041225, 14177885492912233756722387608559020759985450365380409821785116966278703584/2636445214185484345312935218981687142875)

Commentary

No commentary yet.