curve #4064

y² + xy + y = x³ − x² − 555650449739322285903710817508342102232389660121887577x + 159419090134568838779583318899772141333783772100147471568592451817299816049638201

a-invariants: [1, -1, 1, -555650449739322285903710817508342102232389660121887577, 159419090134568838779583318899772141333783772100147471568592451817299816049638201]
c-invariants: [26671221587487469723378119240400420907154703685850603681, -137738093876267476705559987409382632968695565339325878853461984287950874480559689329]
rank (lower bound): ≥ 20
torsion subgroup: ℤ/2ℤ
conductor (N): 3837790555226969705537890168396950553913036309626451197868514544063254214128052127345730
discriminant (Δ): 520418166667252556717274849492677873051726682716762657029268743555407094166711165918928549864678842479965582414584854769333963646354290226075542790810000000000
Faltings height: 29.5583
naive height: 382.8695
primes of bad reduction: 2, 3, 5, 7, 13, 17, 23, 47, 79, 157, 197, 239, 283, 331, 479, 1381, 1511, 1531, 1811, 4111, 8783, 16943, 20107, 32653, 36901, 135409, 17470571, 220570313
regulator: 815793069495609217801333.929689388203129074788628909471382226250608478550810189
submitted by: wgxli
submitted at: 2026-10-08 22:49:30 UTC
last updated: 2026-10-08 22:49:30 UTC

Witness: 20 independent points log in to add more points →

(432078302660949180106100071, 1533771152551474318303051447755120844)
(427164345882465141186902871, 97169425656875100458580934360344399484)
(428500885943058218671541871, 26782132371092888445187035836438981644)
(428629931177853749698188351, 10853604905540053351689016049226613324)
(432150590733308795761765011, 18137449530205624832630716228342501804)
(432787840639794116190023151, 61600836124848304295816151450198558724)
(410254963781353049462651571, 714418092724881977730498004099644204844)
(426901766091582349775462889, 108141116053885715194095118699260908944)
(442527088511925363044039601, 434618545418565305743322488893756924574)
(445109096843167821814248951, 529124643476412547460386196833078888924)
(347551626865134292801983351, 2878085268536866923785007967068365023324)
(464860688995415869560913455, 1254322021281824672055272027858989733572)
(498556157632622350421465601, 2513240768685245008056020981621808083824)
(550047586757743154895228801, 4494784743876102225626232191765583676174)
(654940099015079761147423455, 8742746396574027059119031085841898610772)
(-642421640272080164074268849, 15850866795556936963683410095693924242724)
(17875339001592658666032150351, 2387863842619510111129900296381059468989324)
(209675581135948700630528227671, 96010568737079205464678713509062382121205884)
(2204431606983117611748280323351, 3272991813925113733535609839657585730474593324)
(224482638080571318660998244541/16, 106211827497653171646191988173475412204284561/64)

Commentary

2-isogenous to curve #4063

last edited by wgxli at 2026-10-08 22:49:30 UTC · history