curve #4139

y² + xy = x³ + x² − 141429751975397185737887x + 17291015394305651941273445510693361

a-invariants: [1, 1, 0, -141429751975397185737887, 17291015394305651941273445510693361]
c-invariants: [6788628094819064915418601, -14939437300730997987971399908104703349]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 323788667062716788509227224771003990749916264503469917156290030
discriminant (Δ): 51892557356973665864811192325568303834519142484111487345407845165502500
Faltings height: 12.2903
naive height: 171.5319
primes of bad reduction: 2, 3, 5, 7, 89, 45456781, 11101376325725448761, 34330239985218869606917125915307
regulator: 149599733340919569.36270760255014744110421429438165472289257262723587772513
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 01:06:56 UTC
last updated: 2026-10-11 01:06:56 UTC

(49126977981, -102281817067044708)
(301545839178315/841, -2746060821813723888231/24389)
(-50592630678445588/192721, -16125373483670609979748219/84604519)
(57556448651926052/185761, 4540005599058887010498799/80062991)
(-244608021721052/729, -3232389606475540033423/19683)
(13236979063508172/43681, -434095712933821302943599/9129329)
(7316104068290, -19763095960975271161)
(6479084020313690/97969, -2781330172096636868149573/30664297)
(-219617441951398/961, 5782585840272958812149/29791)
(1446414265353488978/3829849, -998434735093685981620967293/7495014493)
(52479664115813/49, -358815791138015092183/343)
(1388238132383206367/196, -1635671009075851998426186779/2744)
(3631326814429602642/7070281, -5321912806658959842413297619/18799877179)
(5679864365959602/19321, -89868110023643759229339/2685619)
(125749599255255955617/211295296, -1165151188635354563532624930141/3071388422656)
(202637592794633290002/171845881, 2749930141432664707852496947011/2252727654029)
(324537832980, 74656345516124811)
(134607090702482/361, 878319283259302370621/6859)

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