curve #412

y² + xy = x³ − 307611847416435887033706352943575x + 2290502402472665291747329823139073039386938155625

a-invariants: [1, 0, 0, -307611847416435887033706352943575, 2290502402472665291747329823139073039386938155625]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 309727549329348850674760375714963991618334001936196477335817873914413353415870
naive height: 236.2289
Faltings height: 17.6549
discriminant (Δ): -403547036329996664856294057469148964220541602594829834970965447101266596764264930795714305024000000
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 701, 6684379649, 88946362963, 13037969168209, 15949984755629648188802279538248377
regulator: 854393737192105665425.37009655219411154479830193859513346038552939093847629988168
submitted by: 7fff-zip
submitted at: 2026-08-29 00:00:55 UTC
last updated: 2026-08-29 00:00:55 UTC

(-16756188758906530, 1655376636640442636659205)
(2590073142387350, -1229284618127165206876075)
(219668431491669500, 102638426735946904649136575)
(-6873239417783350, -2019923432431470962549575)
(-55014125424913052/9, 53610034287687747357720829/27)
(-14734718247561388, 1903678895032010189267927)
(12990530150921390, 697612856732150881580525)
(-15453558496452100, -1831310343567027563782075)
(12509108112644856206, -44242442228772730558673782363)
(645828551422250900, 518820945906411747228451925)
(148711627697613782, -56967751753047161705825323)
(12910733264283350, 686337897688757648592725)
(314488068703960400, -176094530519452446846577075)
(31067971673529695/4, -4865133892459848489489275/8)
(-8183624421200350, 2063930942534619311086925)
(9863484369772100, -464736076050125933344825)
(49673453251188470, -10467913817017129272577675)
(-6202795736296798, 1989951085000117708191821)
(-6122652124875700, 1986047252070625969180175)
(-4645106685255970, 1902410239247238150608645)
(40909697197712975/4, 3702679865521182488781025/8)

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