curve #818

y² + xy = x³ − 376988648677217532678491040521012531892688856551972615x + 69359739347729558612212653658573174407555441706271751315216539910573939485561225

a-invariants

[1, 0, 0, -376988648677217532678491040521012531892688856551972615, 69359739347729558612212653658573174407555441706271751315216539910573939485561225]

rank (lower bound)

≥ 29

torsion subgroup

trivial

conductor (N)

272022694558381105071096271929883005764754710431026550242052206883045271067121205935580115127054876356847008806831483167065787410

discriminant (Δ)

1350724630602550900193634890024942787942038775540942640517843661024293737638979296277800611234685097927473230908684097918098687459493580604778681078158926720000000

Faltings height

29.8225

naive height

381.7058

primes of bad reduction

2, 3, 5, 7, 11, 13, 17, 23, 29, 43, 53, 197, 208178095561, 21119527672039, 4263982354803745219396720373, 242746574875395303317789636869432622625012081761855257456843

regulator

21781550384424473703962784861906044.1908534545946655561452271580554630707831780039793988829950458

submitted by

thomas

submitted at

2026-09-21 23:36:01 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-22 02:45:46 UTC

Witness: 29 independent points log in to add more points →

(-276455482890814125492239170, -12347124353177608298373561542208551839915)
(4375492797593165075347624580, -286685164503853260095545757478783368809915)
(2093384903764841015684037290, -91945282997500991991254021269298391988915)
(-51460076265165050706754701730/169, -27433415560006363715400030335110253991457255/2197)
(-690280770746176292163457270, -823144129312816611568565591704759564915)
(702850373397797845484172230, -12312605761213865461510737434822526712315)
(563423790975813077762410280, 5984329701734980592038258227985174447085)
(-424937559969771555075991300, 12362223933161900994803850519096360716015)
(34977807105341752054185347270/169, 983673649493906771816241964286851262104745/2197)
(237191326664552588914930499120/289, -86891754924186015934266158387255175542699645/4913)
(504017077091339572025487830, 2718106059201760680282354513051354394085)
(4049386678096405824161504150, 254838647893500328847786274522486869981285)
(587806578898952709651135830, 7131637043245500589808342915549680954085)
(-84444568304695483949941801330/2809, -1337124824915390783950355588253532651657398455/148877)
(534968746229324225256099830, -4559181325456279474803273704798716645915)
(932581582358528672297355950, 22996980495864264431742601096835148455285)
(945695870357344667239408730, -23635088706084350566396664171570471337415)
(154008577870738000524216710, 3866927465557275367175105499426806895605)
(-162842881776233534316552121930/5329, -3497935096452479075876484219926585908301515555/389017)
(-643289855376017178136970170, -6757612174143406453746337248463178545915)
(150284799577504626202757200430/1681, -415649958679923514560670976216118526244689715/68921)
(227233753358974331027358188630/1681, 314851894402584468251033262721101144480748285/68921)
(486883685011920403826660440, 1108458708491532042910949949334159875085)
(-2630491233037266539618517291130/4489, -2838255738786450534103719398737850779079013145/300763)
(-650716842424918761849527957890330/17698849, -679050384667664431592833859589769757916943786769845/74459057743)
(1415179147238843241887139830, 48683445394491521035521959507756016154085)
(3115536406098604098338197159130/6241, -1163582466180591634199005938118205101216554685/493039)
(-5845306561061002075376145530/9, -171277126547908567893527994765345558859705/27)
(28027696486542886824926623003430/26569, -125933805412724954287204029772864003192734828985/4330747)

Commentary

two-neighbour fibration

last edited by thomas at 2026-09-21 23:36:01 UTC · history