curve #2011

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y² = x³ − 10830349308470718990876734667x + 429265014595856916001459704411376552218074

a-invariants: [0, 0, 0, -10830349308470718990876734667, 429265014595856916001459704411376552218074]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/2ℤ
conductor (N): 425237262681943850014675499511718426424003280
discriminant (Δ): 1699177272342796854597670852897542614297767319183014387325881905914604631586400000000
Faltings height: 14.9732
naive height: 205.2701
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 23, 47, 53, 67, 71, 149, 337, 433, 509, 673, 1277, 2371, 18301, 178643
regulator: 24824671629571747.59095548004397186606451649531885076016948485652
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:59:12 UTC
last updated: 2026-09-26 04:59:12 UTC

Witness: 13 independent points log in to add more points →

(5531017794157786592289283710735354520572378320347561/84088311877277591376791231386977678400, 29536651510620812280673442153091577886688060913348917694158366924786662028309/771087123386098119707077312826933095947455526452613952000)
(9760727224701993937762162269465270227267418635231/10173291742389365046230991026292025, 30322157232328408959662155087557915405562003530851223840735323850856749746/1026106050811558410470159430826049742553295267990125)
(4259426295554771544914326676971543/17128597737291762121, -256710742396686231459015590315169350190667203341250/70889630914409609539290574331)
(150896841720317649061077022455501934728779044562562428977/245307631323557127890244130490224266928144, -1828631408655092481076258024008738944960017085007487764492261591446846886169486850775/121497289261616127674881782372323179004788031246511276033294272)
(6781435821135589426053393495861640032861348337/96206929782995642982051017548864, -119657829621313591767187619545221868771469368281350254595998456104375/943646933785242325067435621805471673036562533888)
(4528245087734649926/6889, -9521793539220828726899776600/571787)
(105551795155583, 679760182889232916250)
(235589016169399611788000310713/3398487042343936, -21349408958551401263760133200755109027514925/198120049397433128157184)
(404318483990759200285658697668231993756863/5302553454854333153054178961, -83506220241947447695447869247986497330974580474018139551145450/386124699193560314386985425695785194193209)
(142042652907775667878938366024262/8335924277446089, 1692856250729713915366926552225376540850347870000/761080581521675889032187)
(231375677625914578578596433367/4717397209849, -111294980747934573994296236051505497750062350/10245983891712004493)
(369204775334830483166902/824436369, 218745987218039073832504305870044600/23672041463097)
(18589405836666823/81, -2308911274494584786718550/729)

Commentary

2-isogenous partner of curve#1923 (Alvaro Lozano-Robledo).

last edited by Steps Unbounded at 2026-09-26 21:38:32 UTC · history