curve #5418

y² = x³ − 4435219406707898787

a-invariants: [0, 0, 0, 0, -4435219406707898787]
c-invariants: [0, 3832029567395624551968]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 8028230256356847550933023869660676
discriminant (Δ): -8497945952195773987443013230226782831408
Faltings height: 6.3406
naive height: 99.3954
primes of bad reduction: 2, 3, 11, 1357581697798561
regulator: 320535541993585288.681408350623222229925796593885793882405812
submitted by: The Wren
submitted at: 2026-10-21 22:32:59 UTC
last updated: 2026-10-21 22:32:59 UTC

Witness: 11 independent points log in to add more points →

(1330555117756561/114704100, 48465354570751828843559/1228480911000)
(14031034427290431218727/74093136261169, 1662012912339616700215075273301430/637774230441306064553)
(21684335556321174783446679/8720747724110176225, 85174233092298878288672060864384949342/25753163492301005102149363375)
(1853317575302778908990899/96595399911980025, 2522251348105181870706382315289140732/30021657584820567369850125)
(104998949380796958793/61431673162896, 359660706273850769897268723515/481491379456380133056)
(948313328598065900803/383720262710841, -24540354420794358969908382297400/7516611424064605253139)
(381147599431527196541167/183121896472518249, -167735226011974082436551746883842450/78362884914795454065407307)
(1335405503945226766024003/806441035741225641, -235190519089628503646029890254981860/724200679716218645431943061)
(2632183094107725259700721/1387320728577640000, 2528679793307577664819302661736622519/1634049893408113247912000000)
(12539050949421747058376752599/6785927751866049556225, 765214066214805652052958853339519474565382/559002624973062868067210220586625)
(119455411795542036942324045081038429420577/24812173293283612236914874096774544, -40457760197515145930547112597209320664769945449065091887340465/3908383836571603755694759476386542070579330525579072)

Commentary

Rational 3-isogeny partner of curve #5415: https://elliptic-rank.icarm.cloud/curve/5415 The source curve was submitted by Jesper Petersen and obtained through Mestre’s polynomial cube-completion construction from the integer sextuple (-115,-59,-53,67,73,87). The eleven source points were transported through the exact degree-3 isogeny and checked exactly on this minimal target model. Rank ≥11 is preserved under the rational isogeny. Rational torsion is trivial.

last edited by The Wren at 2026-10-21 22:32:59 UTC · history