curve #293

y² + xy = x³ − x² − 5903488565485287740438969673369x + 5518803574595815094969270147112053094136508125

a-invariants: [1, -1, 0, -5903488565485287740438969673369, 5518803574595815094969270147112053094136508125]
c-invariants: [283367451143293811541070544321721, -4768246288450782966899919262282661938516493572269]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 131631975682729669389442024377793851822199183556933579903854053067329840210
discriminant (Δ): 10078355558706703684843405486969180737019976104948265420188700925428061751697320915371210000
Faltings height: 16.4206
naive height: 224.1729
primes of bad reduction: 2, 3, 5, 7, 13, 23, 53, 3815107457160822140361990058741, 3455946553475218426354730105702040521
regulator: 24356919121296707315.15165264735381718991392031385298104448996945713188874177
submitted by: 7fff-zip
submitted at: 2026-08-23 15:36:26 UTC
last updated: 2026-08-23 15:36:26 UTC

(1153962276197966, 15590061283517212044767)
(92100776408271820855886/64625521, -11756203137872332595279472542027/519524563319)
(1656974399424327686/2809, -7048826663907359406564682577/148877)
(170853120603735380331/119716, -26149601466307281046227056663/41421736)
(2036324213888454650/361, 2671488164148698165218256105/6859)
(52045425282421240375866/37834801, 230318053795743559319846493026117/232721860951)
(-387620982647256199/1849, -6530805308785278432057509551/79507)
(116761932322118479481966/79192201, -3139007439401878275466064644224367/704731396699)
(3518633130624337606/1089, 5104564272374490805455198239/35937)
(7821602911300970345951/5669161, 4744130174699630286658453860172/13498272341)
(-5122739367011642854/1849, -1960759622511510351473743807/79507)
(36101344374083526408147014/24366273409, 18834003941185272175584570081515362811/3803502180324673)
(1425176439496694, 79784480532978603167)
(241310004877282759572374/123498769, -52147181441142359179758114232456621/1372441819897)
(3547324245627306, -170923970544158841145013)
(1916053915048029155171114/196925089, 2576398997211302771319976902012025099/2763449773937)
(544733405411415010019654/336832609, -87697339031030636293995914453483861/6181888872977)
(184090515155501921606/72361, 1624573563927306285181237669963/19465109)
(233060677283881646/121, -47874745498407650705168243/1331)

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