curve #539

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y² + xy = x³ − 6902067553778956712565448576054981155x + 6983137589519946475956028156277280282511573594784076801

a-invariants: [1, 0, 0, -6902067553778956712565448576054981155, 6983137589519946475956028156277280282511573594784076801]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 95221940916620808088830143485247567246687065418433849627482469977720285740879030062
discriminant (Δ): -22657555687628004308985181650141782410370492387253292952342791815938266257441495136149720219561436418899181568
Faltings height: 19.9254
naive height: 266.0893
primes of bad reduction: 2, 3, 7, 11, 13, 29, 31, 61, 71, 647366663681, 17977278611323765757, 31808036444324366418871855366036370478859
regulator: 349584653800307350072458.104124088883729865237410531408830732939897458508343252422828
submitted by: wgxli
submitted at: 2026-09-02 22:38:51 UTC
last updated: 2026-09-02 22:38:51 UTC

Witness: 23 independent points log in to add more points →

(3531604474263556741779438/1692601, 2841858929181492730506728474099134293/2202073901)
(422482000374643758, -2035324921342327772586403287)
(-3032369612718864474, -171213076427496467082417759)
(1772504588232403728, 563912563894121065426631439)
(21808882185466692474250254/14922769, -7632162157046730735005453734258816353/57646656647)
(1549261149044900910, -92653927529129385693587031)
(380227744357102806, -2100892841375136798368536239)
(1510275849535687398, -62848146987298932307413447)
(1511514978459851802, -62316991624546425632900571)
(1536470602771804710, 74325264981816808823666721)
(1626475717188754134, 244558799292039678165974865)
(203490106801566690526494/133225, -3177636106582734473107573018150083/48627125)
(16979551327040281516431870/11296321, 2577158292108305058965503704455704809/37966934881)
(1410245947455787914, -232836752606237773689183339)
(259986494989856154516/169, 168545448033412687706235342525/2197)
(3155236050303270897774/961, 132277886908728539966674214740791/29791)
(30219723056250886254/25, -79671365644904473375261329243/125)
(17270144296103404680085338366/7001505625, 1305534563294627026690329918604427346134811/585850983171875)
(302469170703705594094063186067422220721374/104776468921936989355369, 113074875319941126184499055168570340714761729352493411137642237/33915297990126535912886372981708597)
(96713070006976463149914115374/41589484225, 15885277186348552303077581640327415500397623/8481551465425375)
(1909373662069195851543296977659208590/760984767913559281, 1551343349093822155973809467637482558812521842034625649/663840807623556034070409929)
(146592217586171911780075266212190/87741644436601, 278971520750964510501665484382573795289932253931/821880458261507833651)
(2713334925765244556437004079147822/777381889901761, 109266450670775425689467404206554158261161796162761/21674626802646352543009)

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