curve #499

y² = x³ − 1527601939027206711667013692x + 22645025924456931818524848576223578060820

a-invariants: [0, 0, 0, -1527601939027206711667013692, 22645025924456931818524848576223578060820]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 1205566562821053836690765873262011073495105708451623172030900660673624
discriminant (Δ): 6616411203648005074052562785192246688778450438355614283666008253378589714325196032
Faltings height: 14.4981
naive height: 199.3941
primes of bad reduction: 2, 7, 13, 17, 23, 47, 1585204468285961, 56846000108467905145057461205393515881209999489
regulator: 180764258771391725827.620594271142433654877313898466917971084005459144907993539
submitted by: Rayan Hatout
submitted at: 2026-09-02 10:33:04 UTC
last updated: 2026-09-02 10:33:04 UTC

(5512783168645484/25, 403271946727621176028102/125)
(42369378374920561/2209, 2079748102673750194564333/103823)
(-29501202258908, 205025866108236599062)
(223826423900962/9, 161889052863447469378/27)
(23233115868806794/529, 2441550742256039211575414/12167)
(26995740820994, 32862844454737394266)
(-531887961101316726/11881, 46873967299004681891298334/1295029)
(51177441651306, 280190411868462406822)
(404807739236308/9, 5723163024883547803874/27)
(-6916617808974, 181328366391950184602)
(3172034825094817/9, 177596198551046334201947/27)
(852812072706252/49, -12509378484477604369198/343)
(1889312845287418, -82103863782155810031514)
(266224641504714044/9409, -41568471518913920055610226/912673)
(962416009080417/16, 24653972525071765205743/64)
(372272682185510, -7144655072888138627170)
(4113779552505814/49, 239152668961765891387406/343)
(8181120482751726/25, -734922634850555434263526/125)
(35262551061410, 112361095439724590810)
(127862730652477910/5041, -5267981051159130076112270/357911)

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