curve #1896

y² = x³ + x² − 30996217473478762452763372793456730513745x + 1984633244436782048821649371709042576435200169261463346999475

a-invariants: [0, 1, 0, -30996217473478762452763372793456730513745, 1984633244436782048821649371709042576435200169261463346999475]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 6249795073385897260068400462109947674300086869990618248769385186225304900224010682606786378937672760
discriminant (Δ): 204377905974306278502273767902498475868846539413430879250049332631381279695722379104511535856605700297729298690944340000000
Faltings height: 22.2207
naive height: 291.3177
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 29, 79, 83, 1307, 253867, 35853998647535405057428940725487592684168221764061169442040505022008479097086743
regulator: 3972388081735817107050718550.49040761664034931793102219996054744846857879104250021018540959
submitted by: Ritik Jain
submitted at: 2026-09-25 17:48:12 UTC
last updated: 2026-09-25 17:48:12 UTC

Witness: 26 independent points log in to add more points →

(72996836368639181319546273590/565345729, 4940208101171736357818485339919369850711525/13442225398433)
(-7933680481699159601601688452167298852764815/45819695333393161581361, -14416124447752291893245963717438042054571910821664154061221521050/9807951185816662268249931494221609)
(235436758035459936542909435/534361, 3356993670395136086343553517021485405950/390617891)
(2736681960210113161267811/7225, 4100813939719917760670145033174894366/614125)
(-139409585479492645690, 1896410621662975358987626566525)
(81465521563664444075, 12916806465917507140323288810)
(445236714326946719224265/2704, 163077136068439677100678106081146125/140608)
(1715795820223378630739765/4, 2247493123947575563714921528194128625/8)
(219285217263740388035, -2394195344242157212479804561750)
(152453133806790732785, 895808064542322375427343967750)
(380118375744432181745, 6717566356423647407924500291590)
(-7861917671514916465, -1492594054383168560031341357250)
(478920654826835590535, 9848225089507964271224034210750)
(327136820119820412220985/4096, 35659667248765634219097382636870125/262144)
(688444688639240813264735/3721, 364805001175948671862800398026154250/226981)
(80114332926639998233790/169, 21280364710290811988342547713155125/2197)
(61079823912104676382159610215/492529249, -2392718494138259603065832758041551561873250/10930701623057)
(-1291089430478643756349302813690661/12683106982225, 91293167035248231677139770432361808388285147240538/45168792804542270375)
(57883274770636845254523000175405341305/2601394703908728841, 4794836845219331694250463848368196235430643065788105188770/4195747820178679794634307611)
(1866468482579019807319686671922200589980665/23539389030748844445361, 575768217119996948896938023432734513504473644232454351076062830/3611542913804980191536228298154391)
(-698047493239363136974050726084466480258658766515984308562875/3467773162672492707030339820510133300644, 53076316083630229751603844774976309710009831464760157493846910591633704128058820081070905/204209537567131940477407571774785131180097098435681189839272)
(-36450778864091594255196938297474410163897598601/1102657899578574253223205625, 63134990493321861248656660857815869721696335562241683448037886246884518/36615181371479382601974913546077189578125)
(2024885778475766710609835/14641, 1037791854265456908750257159947230150/1771561)
(-164257914284518291504735/1369, 101006401993308258619449215306852550/50653)
(87471624017942564879861718426450524416383975197372177/1611031435130496277189000800335569, 43939615862515337949056992507440515756227511971118239593722478312316689756403962/64663025667987331157876554408940632775492500006247)
(44720775964681888214181633960605412498963575/174404624908189696355449, 240424990475110456303390234590653414696893480009745520071618797530/72834475352911682066027515082406707)

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