curve #296

y² + xy = x³ − 319020439671592793251066477890x + 66819798277603180086575284892786103016220100

a-invariants: [1, 0, 0, -319020439671592793251066477890, 66819798277603180086575284892786103016220100]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 759280171860352429169339186568850162976568979767271197261226291661130
naive height: 215.4188
Faltings height: 15.8759
discriminant (Δ): 149121443298229386052318979969123375106547503463352849487930935295933405263138806456320000
primes of bad reduction: 2, 3, 5, 13, 1451, 125813, 10664598775761565745369679253752040777416407076555829244209
regulator: 10572544441097282872.83804664175026364445855359725421976142196197372792463104
submitted by: 7fff-zip
submitted at: 2026-08-23 15:37:08 UTC
last updated: 2026-08-23 15:37:08 UTC

(-641163282803604, -2790689375537373120498)
(78416218488938852786724/287743369, -1687296496579759260665684287443846/4880990768347)
(1057011624408260610/2809, 35404874060516057174381370/148877)
(-34718091841930315644/93025, 328312291519718203195476093006/28372625)
(5186245179501891876/9025, 7338412849642871065658901714/857375)
(24507919608191560275714/55457809, -1439112927070943536735565829953244/412994303623)
(716309615268713304/1849, 93138267387050325502205454/79507)
(506197635565182039982692/689115001, -273652306803859605908444498399074614/18089957891251)
(-64886631407169684/121, -12176035860378255458651118/1331)
(455586477757219889113572/1089066001, -92130902342106193898389299179291778/35940267099001)
(-723031030271647740/1849, 912686624408735731081684650/79507)
(2711656762407504/25, -723413564732445325046118/125)
(11938928485033080, -1303076828576504605279590)
(1706248288391402520/6241, -93829605102643633395244110/493039)
(1908393487541976895380/14600041, -291767539533733351592522083393290/55786756661)
(11370494899026463260546/42445225, 211131565016290521632982481377636/276530640875)
(70289807755063655669220/6105841, 18613356808054861901104754673172770/15087533111)
(269682530650830, 631830409106574839760)
(226528739796240, 2485333575491364023310)

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