curve #5545

y² + y = x³ − 454838713910433991443861371850719496163

a-invariants: [0, 0, 1, 0, -454838713910433991443861371850719496163]
c-invariants: [0, 392980648818614968607496225279021644684616]
rank (lower bound): ≥ 17
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 57421671713226472880035373365716817843569590002203716018539056992049
discriminant (Δ): -89371406450173371714049488057673520758818377210766441331493141985942187572978627
Faltings height: 14.0201
naive height: 191.5492
primes of bad reduction: 3, 7, 37, 83, 103, 1140779163383462366684719459
regulator: 24715450088031064114.9506481440512338520707991213553978387395078991300962
submitted by: wgxli
submitted at: 2026-10-23 00:48:11 UTC
last updated: 2026-10-23 00:48:11 UTC

(7774413845107, 3880541610320033480)
(7804701406957, 4535626109678188430)
(8003114835927, 7599971544067729579)
(8107167007387, 8832565692671942784)
(8449743131137, 12184309152562235909)
(9881109073297, 22581328108035406314)
(32726378027427, 185999004957817239079)
(42481311647665, 276060796384234356021)
(235571539145397, 3615569165301401828614)
(69357494811193/4, 551844109792369673617/8)
(134411348622705/16, 751871828522138884969/64)
(232159802356671/25, 2325109562789408395844/125)
(1213926337907017/16, 42272918703294238030235/64)
(744437786623629/25, 20135822529195449168117/125)
(4998898584360681/625, 117782868593745580272421/15625)
(124631967710163201/13225, 29729692996120487980175926/1520875)
(8482315532780204269/55225, 24702697317496373820341733522/12977875)

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