curve #298

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y² = x³ + 1000000000014000000000048

a-invariants

[0, 0, 0, 0, 1000000000014000000000048]

c-invariants

[0, -864000000012096000000041472]

rank (lower bound)

≥ 2

torsion subgroup

trivial

conductor (N)

187500000005250000000054750000000252000000000432

discriminant (Δ)

-432000000012096000000126144000000580608000000995328

Faltings height

8.3949

naive height

124.0472

primes of bad reduction

2, 3, 7, 607, 1667, 8331667, 117674747

regulator

15748.6749446426803068338929550052004216109

submitted by

7fff-zip

submitted at

2026-08-23 17:29:41 UTC

later contributions

rank ≥ 1 → ≥ 2 · 7fff-zip · 2026-09-10 17:41:27 UTC

Witness: 2 independent points log in to add more points →

(1, 1000000000007)
(6234959665401934515782858946117439070836757242010930067966949773313313266993664453325761309273455592129765083559602045782458211339768068872259557973242145723221358020212177291534372285776395892219692265165283956853030855352590939168510275587078152073080454790549505513529658072752016275753472045359654172122938670141137094342544141807834463191261967817514067011833/49043826775388978760569212113286693345092000291716712635197177787923956163063369104467249975176224194323375825632651863448822387607159250466282353512329091811315506990862461830625710353699901208576339674471627678828641212802759957129842281034552787831267154286060000833456726509892521435035850731700623099658150796056119511824208664327556352063055339507364, 600289339035971133896452827852375749082546769554573681618162067497600723419952378260845986304017427246174315464603388955719584478488593110521442495055296356817053676569883564613094654695731511518416289648821459276010136351503853286181953789880886051181423302213548183336844641293101987575399938521120553628782929745364415758598383046663158412707667472083222124806089215264162851835190678422805341272932183274312352615638758472443412410698237010397795287359652278601418838581792710509372758483758732208696371990113046678407650556849602408933590157/343460284025513068604573639072085970761631462433051030977651769455425362746631827425234527222694007607901527710541460161851236755363836582712330423332485964568524650906697242826929247809195561201118613577947295167924535486555192940200316210342188635189828992516034359676778868071377889492513752341115397471555202638517345695734796381497328364221982613197200760501614477644793147122577446401722277535997576531551475974555099377772585214821648245406702896748077480700032736332962314237447196913017765592523079432718755416531418630956888)

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