curve #383

y² + xy = x³ − 202780642049313963986778660430x + 34519698985201688159263901059751374440368900

a-invariants: [1, 0, 0, -202780642049313963986778660430, 34519698985201688159263901059751374440368900]
c-invariants: [9733470818367070271365375700641, -29825019923214273169810238066230594564542280561]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 1084369031554210976299817632044696526393610580197387810291847110970
discriminant (Δ): 18878259596012030370825791301508298938819182134584892984497388982367104183322924800000000
Faltings height: 15.7292
naive height: 214.0594
primes of bad reduction: 2, 3, 5, 17, 19, 31, 37, 617, 58687, 144983, 29917627324201, 621181635174315184278462253185947
regulator: 260215329920993642066.27940022190886312558504614426053498525657585766294725
submitted by: y011d4
submitted at: 2026-08-27 02:22:51 UTC
last updated: 2026-08-28 17:12:59 UTC

(71794305242088565/144, -13086194511135912918355015/1728)
(1098629235157988924/2809, 577312872803458199451632794/148877)
(7097516675561138/49, 981392268221939784918506/343)
(1475654274117155/4, -25195912484564688350345/8)
(425215702474122140/289, 265544999431388830262083810/4913)
(34793346908360105/64, -4719128041361197190464385/512)
(364797929676818840/529, 181536810478937107127558890/12167)
(20991874823286185/256, -17590469302100525103524605/4096)
(-13712509642446148/121, -9964264831987597753759898/1331)
(1509253957090052, 56270085224749046061242)
(230435788304636, -167548935723428548318)
(-456734872981588, -5644352255360780231758)
(198218923847860, 1453584054670559936770)
(397408797120860, -4086214873392535069630)
(-451128962852740, -5846994959608702849630)
(6790010105478140, -558306257886461890593310)
(364916997072260, 3019197454737858850370)
(74782483759878560, 20449936850823736642786370)

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last edited by y011d4 at 2026-08-27 02:26:06 UTC · history