curve #1971

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y² + xy + y = x³ − 21393306539335272782237159153x + 1147019831058161467873753622085003660012872

a-invariants

[1, 0, 1, -21393306539335272782237159153, 1147019831058161467873753622085003660012872]

rank (lower bound)

≥ 21

torsion subgroup

trivial

conductor (N)

10810735130774092881355313836361103022052853161790071950809664863360411426

discriminant (Δ)

58270914406556171541771521581538485762004299211642345576462999897322860671450431268812

Faltings height

15.2131

naive height

207.3122

primes of bad reduction

2, 3, 23, 41, 59, 107, 8053103, 28763260962710753051, 1306637503297545708053185055555803278073

regulator

423946675015840630592.04234643839453677655774830235599206677112398786243684539392

submitted by

Ritik Jain

submitted at

2026-09-25 20:07:17 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 20:09:03 UTC

Witness: 21 independent points log in to add more points →

(3398779832269312476963827436946018071/3680749479286274087044, -6191430726408656044148936535203838532701251424104776081/223308055042043401900850971454072)
(-37301549822641964/225, 1250045640790680279308396/3375)
(316801423335085188473775/826102564, 166783133863451186251063700288050883/23743839894488)
(3504755898930621/25, 118788683635516388197754/125)
(165459252271715904/9025, -747918631627853235171314632/857375)
(-2850301124799396/25, -181318979701550246081668/125)
(1557106711037337, -61181429228819856697844)
(-147952326244191, -1036122036800618050598)
(109372400102037, 339897586045341642946)
(-2261034975239371/16, 74311046178354480631887/64)
(35223102090947226/529, 1621491797992829577231674/12167)
(7173472643961081312/160801, 34207091505892987485581343656/64481201)
(267719884445607/4, 979382353486142502245/8)
(-28258772371803975/169, -486500361234878497208798/2197)
(224599324047591/4, -2803639791734552209651/8)
(-155026572933237, 858929792352364340620)
(37969013933942010238433415/103078239364, 217631589028522859546850702527020074661/33094093373727112)
(-149517034847732278722612830855990966601120780909/2638124888217242800419049158297721, 199947940968141697174529665011797795072404905386184209305824488871592360/135501164213573298779958127306886009482283402471731)
(2352044762082241374269118890287726485/88120134461120361138289, 20178007581782179944756096383170091308027499312382797144/26158493375169624109709062158523913)
(-66422500517495920158926246852943120206375197754814/649134741861873558478493559956992969, 787061178973304687289231248457456690906157401956619146363251371781211678101/523000711827277926896402586843766081519176180073335547)
(-854631438958992201687271610008588126916025844500970113307679/6196650163325633965325895142946026332901709049, 592249976632228395832444358197076523791574959609619706335998586881292271596482719500637196/487792892030284803774151806300959551056617202527477384682331513430157)

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