curve #382

y² + xy + y = x³ − x² − 34917942850413226144077798077x + 2481898466598513504719028897670995969469829

a-invariants: [1, -1, 1, -34917942850413226144077798077, 2481898466598513504719028897670995969469829]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 112240872660762089670916935090354173180383921463391326427626236830
naive height: 208.7820
Faltings height: 15.2708
discriminant (Δ): 63703131987439372135517846011325677088887341768739771260057668244291152390033333760000
primes of bad reduction: 2, 3, 5, 7, 19, 23, 31, 37, 32963543, 3202443961, 3367054971973339150441368863800537238453
regulator: 42832043429497849268.197411242377522711119580687641284759392002573274679211
submitted by: y011d4
submitted at: 2026-08-27 02:22:44 UTC
last updated: 2026-08-28 17:09:49 UTC

(18141224216989821/289, -3601474082206458223638394/4913)
(-68451192848003, 2133387185722355524156)
(40491137888904783/289, -2864597374998939121676152/4913)
(-65344381139956017/2209, 193927386928720333240410488/103823)
(82506038683087, -403232306125580882744)
(470808351714511/4, 408132489019980164759/8)
(11846829819438039/25, -1201211635716048822715672/125)
(3296487812257191/25, -51579406237177879412776/125)
(206808168014047, 2026249904374802230296)
(12943415084911807/81, 722582847402701954553224/729)
(-196925163790413, -1312042861033126634744)
(620317054178967, -14816056361082873146624)
(682506297330843/4, 9770138181029210353373/8)
(-154913521264413, -2042918038093607820344)
(1504861648441063/9, -30999132378460079522728/27)
(34964931605732943/289, -825935144972858187252472/4913)
(139692564746607, 574529258468944579336)
(958152940500957, -29131842815851506813764)

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last edited by y011d4 at 2026-08-27 02:26:03 UTC · history