curve #52

y² = x³ − 2827529113871322622866959217x

a-invariants: [0, 0, 0, -2827529113871322622866959217, 0]
rank (lower bound): ≥ 13
conductor (N): 28426385385919811326943632130923115672884025713568899872
naive height: 201.2412
Faltings height: 14.8383
discriminant (Δ): 1446775781054662070702764737544843998787085870189239433227587805462261153666449364032
primes of bad reduction: 2, 3, 11, 37, 41, 73, 151, 269, 509, 673, 1193, 2969, 5233
regulator: 108176633204870.8595106109963768445277899866191644600170784154096
submitted by: David Renshaw
last updated: 2026-07-01 22:45:39

(-53023103285625, 29199177719416762200)
(-52826063038023, 44172308695386224232)
(-52264238470308, 70825438517010888582)
(-29162438222148, 240117703609461349518)
(-27920725708647, 239124633951324498624)
(-23843884093425, 232084669370223457260)
(-20893472520447, 223508666443210130124)
(-19924665190425, 220062792377751438960)
(-11023069423473, 172709750574634889268)
(-9645751205607, 162407501940473002224)
(-7293017369343, 142243865194633256268)
(303030650052889, 5193240002220574777616)
(2659109867774031, 137093723243731091154492)

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