curve #307

y² + xy = x³ − 1474705521041100338570986911092165596800135x + 689016723668927095487122547447296652854367658972300541602585225

a-invariants: [1, 0, 0, -1474705521041100338570986911092165596800135, 689016723668927095487122547447296652854367658972300541602585225]
rank (lower bound): ≥ 15
torsion subgroup: ℤ/2ℤ
conductor (N): 113867782999071766513257245176182365522858404266111886760688305190
naive height: 302.9047
Faltings height: 22.9836
discriminant (Δ): 166587152111400413731938961061747813215845690391267294429737525157756851883138882108010598181179320356424466059369807216640000
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 23, 71, 127, 151, 179, 241, 281, 449, 503, 1223, 1361, 1399, 2017, 2083, 2293, 2843, 5651, 74923, 436549
regulator: 2400605753683962035935.6370808782221747390047364372966399052405916436
submitted by: 7fff-zip
submitted at: 2026-08-24 00:23:17 UTC
last updated: 2026-08-24 00:23:17 UTC

(1920603132489760518390, 70294046253440894558287052273445)
(723782690206887954870, -901218737287813014619154687835)
(2030475645808496687783430/2809, 126623800322629262319397573008219105/148877)
(537377864451004159651476630/628849, 3624988630231720910557018341067718389005/498677257)
(2709561841563783846557286/3721, 256839622058000442458041777405001817/226981)
(1817681738643095493879210/1849, 1093999188760892045892340176263152155/79507)
(6537665521251859372800561/6400, 8071411215270300902102938234479361569/512000)
(4114408609701144492375249/64, 8344190238147403965701069397348565629/512)
(13357183332054735368272822/12321, 26107054742682912452222942324188555691/1367631)
(708540232257510799707265059830/779470561, 217185533817632278120066035869566802436642635/21762038592559)
(115230037686332102617337370/160801, 30790324417194837449207975685276111465/64481201)
(55402067611860058208679414070/349281, 13039960282936272991307446218960619010810315/206425071)
(9675409614814254209123349050/786769, 947234294875592705831165242392504956013295/697864103)
(327217993928580102004686624390/275991769, 112978747848613493001718983707858674253656305/4585051258397)
(59805667931279294631790447974/83814025, 166808966784033094273426041794311254178983/767317398875)

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