curve #3809

y² + xy = x³ − 11396409080653855934430x + 475834504626943740815003101211076

a-invariants: [1, 0, 0, -11396409080653855934430, 475834504626943740815003101211076]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 57882727420857162665573258220813467957594529726
discriminant (Δ): -3083539090871657212650011658595663085565289355789353413445933498368
Faltings height: 11.5528
naive height: 164.0084
primes of bad reduction: 2, 3, 7, 13, 29, 31, 22042619, 5349749641148782747922240425504351
regulator: 9853343635084.820198208327906732248714343831451006392220484236057917289
submitted by: 7fff-zip
submitted at: 2026-10-03 04:54:20 UTC
last updated: 2026-10-03 04:54:20 UTC

(18133193482561728956856/344410528225, 942863843438092827826058428182834/202122484646764625)
(-72528095148, -30345853485758406)
(-99684641909508/19321, 62089271863261106617686/2685619)
(859914170701146/14161, -4680078696589675860678/1685159)
(-587451229685808/16129, 59459583499392727875342/2048383)
(122168648827516/2025, -255684117081036522374/91125)
(3336460194045756/42025, -72831391178880939761094/8615125)
(-2142315075640218/279841, -3511386824191378438529994/148035889)
(73877870208, -6092083800883662)
(981716575467324/13225, 9485972970635238234438/1520875)
(-2019616301925207/16384, 5782952828228950987563/2097152)
(-100421006874, -24649289017520892)
(-122635601772, -5390948140409742)
(-15029363275309627044/141871921, -37568340377276665327138062114/1689836451031)
(7269492942034572/954529, -18404682899297165378513166/932574833)
(18197920478154/625, -202940974432052647008/15625)

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