curve #1882

y² + xy = x³ − x² − 3763110016484095148228799773133810982809x + 88650546705548517741048743789172352712852928992846164053209

a-invariants

[1, -1, 0, -3763110016484095148228799773133810982809, 88650546705548517741048743789172352712852928992846164053209]

rank (lower bound)

≥ 25

torsion subgroup

trivial

conductor (N)

605118000845489122076201591639159194333793203968482944269682985269422887169508105629827746843862180334

discriminant (Δ)

15467742663141074644148478330323818445629911393239102527381678075063181455407783456401458795138297505868884887295246532

Faltings height

21.5536

naive height

284.9918

primes of bad reduction

2, 3, 7, 11, 13, 19, 23, 29, 31, 43, 58129, 1534830701839, 168787287345562013522621, 18859614105325328277126913964398140101912542949951

regulator

1670435565917702201818364904.534679394597261525929812561815324055104453857542743604002951

submitted by

Ritik Jain

submitted at

2026-09-25 17:33:53 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 17:42:30 UTC

Witness: 25 independent points log in to add more points →

(55486484239903344053390285363704387649725327/1650050940884834105453476, -24441377892462583961842963019661883248729334583609370157514206237/2119561528364330073234196819390116776)
(1103435573464872130262702261754364945/29170598292524529, -103233401242602555141706357790979217184380187278462016/4982163835697195134090167)
(-276337704302255332813/4, 1100007528039027773534051498325/8)
(643316987373340077632, 16245271716242428925291177191323)
(415394818688742284407/4, 7234664789434380995321211934535/8)
(4409880330358753156048, 292818429973978446065474956785397)
(79558693534010601039481/64, -22413623440690337994456218371244719/512)
(-14607222289941630582047/1024, -12235594852357221305730292496871871/32768)
(126286732352754076016203/3364, 3305417541352263060781185279328945/195112)
(8370316303098272665, -240288510585475937441748305177)
(844338404691481265959/25, -1124009480202924709894147815187/125)
(71346516990544064257, 428185412840729800477172249920)
(3789376611679719356885/16, 226109870417546524299879025708087/64)
(531908905595491021021/16, 1089197791793583579799480627915/64)
(28519618800582273583, -67268473754650114737132260528)
(-1133029276303636677619/16, -301648724811812892049788614055/64)
(5294943801437515602465325780/107101801, 169709993397190406087717622710526379895207/1108396538549)
(4351375193388600465631/289, 924428491852995310073701693325729/4913)
(-221807288541278809595787452954693163807628984787/7956072071688854066887515024, 294223918778217423694769004243326861005057182305165069541604715053099019/709656300547965326781316625297655073704768)
(-8081167420117469527001401376604825784622002566367/117577241876744320098223829056, 6062810058363641653428239529896656027576898896486469902692041766673548413/40316693075780092439066537028099445430664704)
(-13886342916830766761860512800181500/209083531397841, 645749313190421227943744074318975733577362210888467/3023289529707520862361)
(-124537597946487267585091130612/2350601289, 42535702932744854453918222531843230964868505/113964202294587)
(220117326599146251550520876/5958481, 101661689746412023530463902202195362819/14544652121)
(-330548994789958506446827255838762/4933991545081, 2193902176050566836833309593143487862132969782663/10959673125435076979)
(33983229016028979829, 3712696422317871480321931723)

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