curve #2185

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y² + xy = x³ − 18247941180734920258951141060855042640x + 30003290659312870154250577706243953923873222960556857600

a-invariants: [1, 0, 0, -18247941180734920258951141060855042640, 30003290659312870154250577706243953923873222960556857600]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 15001118322851415140610
discriminant (Δ): 58910336676342808543704456716848130230380162225496102469172728202030304903488652116057688045623705600000000
Faltings height: 19.9270
naive height: 269.0049
primes of bad reduction: 2, 3, 5, 7, 17, 41, 257, 65599, 74209, 81919
regulator: 622489.68453366341655148289649564670034505006
submitted by: Tom Fisher
submitted at: 2026-09-26 17:31:00 UTC
last updated: 2026-09-26 17:31:00 UTC

Witness: 3 independent points log in to add more points →

(2465691851312622880, 696043088391848153696560)
(299526139374311133233496416291788297474720/121494563208085746024241, 89760059383324119916982236967929464095424322071022523698480/42348230280965451005863362419157289)
(255527827197603823692011696953948551106951690366701807000824460296857544191109177529553040490611277793232865334429328712723331209912026266560051735874593651678513697145420096520365957390391994740532194386646007444478507059729407124477574209059308535275984445648944973857230/103741345948284136600850705022998442002558109152508256758777623996807608081546842897751883462637271251523924738965290989759687615869601630298197558014492384361761785748086947557477806560219345196436037328416193242420156187936018082106090908492627291349969, 8992236068738592977199417717217168961723342142250581399387476637407351248957542689994258388798686468751719255160174869873244536035971856742110190408345123771373528044331860080447724136172230521346777659126418571630040991933558343397019934246107684499084537550620360793967011092035209774250967253346849204690975758718990696148201123874043382645837168758139928716460061585885269278104241162284541200977586790/1056641873779396328820827179162484245273675046949791318104395249215045001870176172014452659115627601514048849596922228268202511367527045717849698016863150848882070412107024720247414591543688472144146764400298035859221663365795113018416176468950462518263225824616334743029549356055831440152227797493555339799615879533493978750678783291869212439586700180038166469129665579881151478297)

Commentary

Found by Rathbun (2013)

last edited by Tom Fisher at 2026-09-26 17:31:00 UTC · history