curve #746

y² + xy = x³ − 1322791863836678632756897906456499538x + 648069501075857258662767528794908106200954623218194692

a-invariants: [1, 0, 0, -1322791863836678632756897906456499538, 648069501075857258662767528794908106200954623218194692]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 156889111317058904627359095900392258545849757386739107494369298910894227152978519034867350
naive height: 261.3348
Faltings height: 19.7486
discriminant (Δ): -33303520599931763950103061542094412347814978171853250595158989021069462122510537288328566558809969494784000000
primes of bad reduction: 2, 3, 5, 11, 29, 37, 43, 61, 167, 687437, 567870619, 15899278987, 5211124590731, 5947074660082643, 1051719181626496323255151
regulator: 1092579385675086141050592.58990996787279366142638341295644428862945670587312542153993
submitted by: Valery Asiryan
submitted at: 2026-09-16 18:17:57 UTC
last updated: 2026-09-16 18:17:57 UTC

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

(-5101196395664243133/4, -4086221822197997251602095169/8)
(-338762010068116138668/289, -3767403259393871212660075448514/4913)
(-1077079444779710148, -907359588065482822411666626)
(-1076035859747408082, -908597516919788045795504448)
(-1007856131996937352371/21904, -2729344267250968542465334696941927/3241792)
(241620708906401796, -585287576597754868962497826)
(451874339617101732, -377627080567319627565909666)
(525828187343488308, -312885388772960289278028258)
(611580663717714948, -260433573676335394503267618)
(667656413423496468, -250033894769071173732350898)
(710734819374025428, -258725110293189064669757538)
(329856858657298250212/441, -2571844791601072222814894501626/9261)
(866040525691648982, -389911807976427593793449416)
(898323614285423802, -429777034195379732476805676)
(2110078476439023072, -2692926671841316104484851486)
(5825073519692283132, -13805654064555492917727665466)
(17156981670173602932, -70910624993846436810357194466)
(23038188017256988668, -110444005757930503358044070970)
(95032458423261948803/4, -925356287126559163321447127153/8)
(26714057554857724302, -137947650352506942121442146926)
(496511762101644132484/9, -11061161963255899007185913021462/27)
(103979339573820672932, -1060215472824303737906197026466)
(525581240898183779472, -12049214757958794746582280691086)

Commentary

Specialization T=-47/80 of the family identified by wgxli in the commentary to curve #302. The points were obtained by specializing reconstructed generic sections and running minimized quartic searches. The 23 listed points are certified independent by exact quadratic-character certificates.

last edited by Valery Asiryan at 2026-09-16 18:17:57 UTC · history