curve #1997

y² + xy + y = x³ − 2473171297950002638486804822705293436825428051x + 47340055711440315852896037477908617292217817446339453623330254379998

a-invariants: [1, 0, 1, -2473171297950002638486804822705293436825428051, 47340055711440315852896037477908617292217817446339453623330254379998]
rank (lower bound): ≥ 18
torsion subgroup: ℤ/2ℤ
conductor (N): 114713100997610410312595038097570863411319285752217220984538901104669511816895282450
discriminant (Δ): 2877796910409261102819645180463063254393245054975605212537640748323145278144637271723411759264887520401633250213968193920294360250000
Faltings height: 24.6770
naive height: 325.1791
primes of bad reduction: 2, 3, 5, 7, 11, 23, 83, 113, 131, 139, 157, 181, 383, 461, 569, 1721, 2381, 2521, 4049, 8117, 13697, 226769, 340757, 522157, 844717, 1973893, 2830897
regulator: 14580229321033280264247197958073.112232451164681942468549564263122045880032
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:55:16 UTC
last updated: 2026-09-26 04:55:16 UTC

Witness: 18 independent points log in to add more points →

(190523286797975472952655386289024/6288014209, -234369742668423715491314177041586143971261160059/498620662731073)
(2311878836007233015812387748557073638367/33281030720777449, 88139316300555015392741908119713105685651936682980468684828/6071488154351863675331957)
(242042192669281175726270906691874412700391808/8405394516695834510329, -17839283656574464090446772000843571656213350854569934941862927487/770614459241182856402813372094733)
(42566365088900903271435216808016/1150905625, 99248301855423656218053888780014610901871626161/39044473328125)
(3425270719581093078872378118552983156851119848/111034758614897530998649, -23483031853404817239886955795146444121895736053696464647993923176577/36998867348098205627684186038590643)
(699017996963799090057548800825175499869298359453633/24238708200120733814405730304, -136828782222717263473351284836166359203083989118287838866198005740048936063/3773672488085167994186575254620652540526592)
(4792722876740190540248082573777671451261778575561392/1371845521154011030046228521, 331764347622093143879100691076595311985777126771632754639742121079491273714409/50811008459735135404977034491702237370069)
(3073028590416970858828414250694056444308063550977570067/106905127055065231257640524286921, -5472423514084949920598865792433263123154829340672362668986066046141594061779884/1105344872601976376673073176175541008506873579781)
(289128414945709442552068211365783283436902848294908848/9607931449134500643982248932449, -12159900027151637429288595525427335593319485364398412485760800683109255682805227/29781381756103194252101553436087662472277451793)
(2032238441385699827692163630137470554458425305051/70589156399417197790676961, 12539616226793286252539936014883258443325438890524037415491102604286144/593071408580741101544537555155459254959)
(7261415200616018099754505548040194008437194452672/241598605570536321260324161, 1491891118589571091251586195974148975570543619465391112198556939215116474/3755274040136524633960848383177730301409)
(165537795532316186025400486114283548683511880736801947/4374078658713432554486030753761, 25787996636741795362301125012303184597213040387258810960692799129059522341177476/9148078507066058696512087368486062893794556241)
(543052476559980004037888866039184901634250275147/18894844030949286927778161, -3311590875033327656589067657692608028263412646837647334875977407424/82132485753585185677440796571666409591)
(12644933986007670074763561526482422861423248049843/436151652269405798640930409, -745457552114747649705179536258477775341074766312405358157840345663266772/9108697577306209068151209704411195886923)
(1874647127083796603765519163629359691339552221849966939347957323/53302245614904578871473610549044828781649, -24182465915032424006871614789400124452724599069304662779419899102492359759145780123403301358852/12306038210615618785038508171015258980027801038529902665487143)
(1399493322141008684550409605734103320434410928648337/45889793468201299735516411456, 5201338651013593524791929024620990514912726929700434049708911541898845486581/9830467113714511219333177608220329671312896)
(48202332927338615411741224651198076541936183875498789114252881/1606843782332858632907080103181956121600, -24484368302622521037363160749320737242485806567660265103329191095643116846438828375162539959/64411065727658953877477555232671933373449859804800372736000)
(556199022816593606479094182816192728570529967586418321385701997603/17655380728327612380510614691570175115300089, 61738215641840266505677925554852063733112890337009627076383131184098710945306565252580011001135168/74184919707431556439331212874539526910705291760095490489481288563)

Commentary

2-isogenous partner of curve#505 (Matthias Breddin).

last edited by Steps Unbounded at 2026-09-26 21:35:43 UTC · history