curve #6233

y² + xy + y = x³ − x² − 403933847800529798861x + 3090440772589271605642422011436

a-invariants: [1, -1, 1, -403933847800529798861, 3090440772589271605642422011436]
c-invariants: [19388824694425430345313, -2670140827429880956150138181327025]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 5126661320120532183815901
discriminant (Δ): 92084152041749294256814298422556193319958162700079706745323049
Faltings height: 10.6990
naive height: 153.9570
primes of bad reduction: 3, 7, 11, 37, 67, 73, 181, 397, 619, 5113, 179749
regulator: 10938653353.843461306751130233172127151229606261344026084
submitted by: apkorte
submitted at: 2026-10-31 11:26:03 UTC
last updated: 2026-10-31 11:26:03 UTC

Witness: 9 independent points log in to add more points →

(68889384651/4, 8915745959219745/8)
(716211097697/49, -190685088246619371/343)
(78267905069, 21235167532652865)
(24677858501507/1444, 59570964735562741971/54872)
(6132114853589/400, 5661925781114926623/8000)
(14548113654697919/1020100, -494532022227081973974573/1030301000)
(330399985156617/6889, 5544753948836264978581/571787)
(21662790045489035/662596, 2687585471656198923816483/539353144)
(103244810728929/1600, -1003213479122666578747/64000)

Commentary

2-isogenous to curve#6081 (the images of its points under the isogeny, moved to the minimal model). Found by Claude (Anthropic) in a scan of the isogeny classes of all leaderboard curves.

last edited by apkorte at 2026-10-31 11:26:03 UTC · history