curve #292

y² + xy = x³ + x² − 64638901051375115282329208x + 199985543623639494018271452767098585212

a-invariants: [1, 1, 0, -64638901051375115282329208, 199985543623639494018271452767098585212]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 10859179694138629484625220674688950147213309742405027569875202309930
naive height: 189.9062
Faltings height: 13.5447
discriminant (Δ): 7198788795422377711047836001349527968822437304655333414525981769447346162100
primes of bad reduction: 2, 3, 5, 17, 19, 37, 43, 26885202676847, 26199303642277241806887087789773747356607883761
regulator: 3278775349212386890.231301612398713012524021120808444504663124124053572828346
submitted by: 7fff-zip
submitted at: 2026-08-23 15:36:12 UTC
last updated: 2026-08-23 15:36:12 UTC

(4065077456748, 2097190988408719926)
(1941722173919954806/413449, -1203990392121368833844110/265847707)
(5037592214757578/2809, -1411049083752168387511766/148877)
(4616649497171333231/982081, -82370259704224427623227013/973242271)
(6541895884410737/361, 484014852268102796327294/6859)
(85866127884691747091/18774889, 12354895492779024315959581040/81351594037)
(-2005675723362031/1849, -1303588184386225996490041/79507)
(21186407691922327754/4414201, -5155672911843787409609575894/9274236301)
(1298379435201676/121, 36253580762696922394722/1331)
(2524260843981244951/550564, 23461802986227205193912933/408518488)
(-16993395035083567/1849, -335013161571105299815906/79507)
(6651073730021416192898/1369074001, 39882955623772133720432444893066/50657107111001)
(6040940238044582892677/491553241, -387110943774676811380699543779433/10898226906211)
(152266329519891071/289, -59409453247373820203830187/4913)
(102467647230785879/17956, -9907232699025271644790775/2406104)
(2794561477092725825021/554084521, 19654837298893876979208087759743/13042595539819)
(38137845356972, -230664520000407690994)
(19629985507259/4, 7839006563699674141/8)
(382564589203588783858/2217121, -7474698811196505404183346305436/3301293169)

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