curve #5765

y² + y = x³ − 55292445628733110921371691

a-invariants: [0, 0, 1, 0, -55292445628733110921371691]
c-invariants: [0, 47772673023225407836065140808]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 73723260838310814561828921
discriminant (Δ): -1320733962837967956150101114693654869537695246701890563
Faltings height: 9.0637
naive height: 132.0725
primes of bad reduction: 3, 7, 11, 19, 37, 229, 373, 619
regulator: 3914670652674.12441068411325587754221381518884065643172
submitted by: Maksym Voznyy
submitted at: 2026-10-24 20:17:27 UTC
last updated: 2026-10-24 20:17:27 UTC

(225283463113/576, 29447908418869253/13824)
(406315389809460663764682624184961976936969/69965579446456227620282079302500, 258960542602545229680147209934144530493128360719927160082887297/585230097162451365859116441759592670197841375000)
(222628909053142179833342748104077761/513676671629085932487577600, 59497258083006519587236204979211703385307559504465759/11642192189701124282925549435626881024000)
(37176436124014876338532901763271788744591451897/12777508281102833909846188815869841444, 7160009607524264610923455736157443404213420152080742249121665903171191/45674021988899771808178278195120021695834425466219065128)
(967198426349764247090892577/48709680904479204, 30079584870157739126121682756107660137029/10750357994337640607692392)
(91227364284850147569436654782958003033/122505047377003595479258204416, 810912306437401716102078115851850896542700208551210402083/42877649900222430130996054392655340703166464)
(617373866987967561353592762193657/26143434857454032168964, 15339861959458514272706509890598872590496786270001/4227114095861637255364048505927688)
(84230148458285457722180247334321/195797004443341480526400, 427264439297547912073330151204780178971181444119/86638128959209425189017622257088000)

Voznyy (2023), A = -2862075021113, [r, s, t] = [6, 28, 345] or [112, 123, 250] for S3 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-24 20:27:41 UTC · history