curve #4594

y² + xy = x³ − x² − 7828643327680369311768856221574537849x + 8445549153272925255126414359686739768487725804283404929

a-invariants: [1, -1, 0, -7828643327680369311768856221574537849, 8445549153272925255126414359686739768487725804283404929]
c-invariants: [375774879728657726964905098635577816761, -7296954468427807418738235047990383388631322151040761683245]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 47136153549875327209902521606877557075193332953476002449626512380596175511770228836436184154770155815337262
discriminant (Δ): -106244890101418987531120283701902013647485772477134909521458158905863779603530095797327159084851931207770188548
Faltings height: 19.9995
naive height: 266.4696
primes of bad reduction: 2, 7, 23, 2588494019, 125933095696613154643, 64152440570581783584216340729850305707027470043201868586139152849251656409
regulator: 62298990933516230769203161359.11067676452399920315253565238369577652733551312842749629051
submitted by: C. R. Hill
submitted at: 2026-10-18 17:30:25 UTC
last updated: 2026-10-18 17:30:25 UTC

Witness: 25 independent points log in to add more points →

(-679701476959012070, -3667788368019888303486047287)
(1423197166622603672, -431877331696636627102904705)
(1674284301317195276, 177693643779886731998530119)
(1842948190511938670362/121, -77866686115678451212336168297005/1331)
(2515021195141232808, 2159788952658333924106358297)
(-76941826222888402096/25, -230068429828662737191076446227/125)
(6445994644654459267/4, 968191785134202264774858465/8)
(-1642593500090446991/9, -84817303653113289387808257515/27)
(43528394313194084137/9, 247039961918410724141126517869/27)
(8533088873112471112/9, -36974681222181825329035902205/27)
(1401596942619793800, -475759748851367234880599873)
(1718681811206907091549/784, -29604428504916261931525846726897/21952)
(14808050482611062167/4, -43963269084956231877296422749/8)
(-2576104016654085923, -3393688098905929763404751832)
(1165733854551722635891/324, -30222275440157484075365336307919/5832)
(-990221892224129638, -3902139359754271717064611575)
(4873358933561445940, 9275463253006330648679476293)
(550241686245939423376/289, -3266582072755506154217276874591/4913)
(406282829716141225282291/133956, -174040516491335280700527079577344025/49027896)
(6326409711454641167, -14564448121012355188133116152)
(27087671477376028341/16, 13455190807982437622319254245/64)
(1751447647544192897049/169, 70864930250836103709840624447848/2197)
(1004589913637867337817/256, 25300454158302956351851596310965/4096)
(3260615507804690444190350287/260951716, 181872076292274044674985192833123706914435/4215414020264)
(1107519765639496034188306602/666001249, 2751515111345806400552780386287954589115/17187494232943)

Commentary

Found with Rank Hunter v0.10.0; family=x1152_icarm4239_recovered_generic; parameter=125/11; local status: rigorous rank lower bound >= 25.

last edited by C. R. Hill at 2026-10-18 17:30:25 UTC · history