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curve #5772

y² = x³ − 449653256189269049883

a-invariants: [0, 0, 0, 0, -449653256189269049883]
c-invariants: [0, 388500413347528459098912]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 145687655005323172162092
discriminant (Δ): -87345237946296567649964044898713050279513648
Faltings height: 7.1104
naive height: 108.6332
primes of bad reduction: 2, 3, 7, 31, 43, 61, 137, 157
regulator: 23306293.74209968210833799634584137406836987556527677
submitted by: Maksym Voznyy
submitted at: 2026-10-25 01:39:42 UTC
last updated: 2026-10-25 01:39:42 UTC

Witness: 7 independent points log in to add more points →

(102314760247/6889, -30398237468590586/571787)
(26898259087/81, 4411472662754990/729)
(2291033124026563/150970369, 102362233384154373428120/1854972923903)
(2954749903/81, 159867503557118/729)
(221414323, -3294576312628)
(3045409169699239/21631801, -168048051570291123710906/100609506451)
(14224498771/625, 1663837357539056/15625)

Commentary

Voznyy (2026), A = 220369125942, [r, s, t] = [31, 36, 86] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 01:39:42 UTC · history

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