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curve #5862

y² + y = x³ − 42208353495110371669

a-invariants: [0, 0, 1, 0, -42208353495110371669]
c-invariants: [0, 36468017419775361121800]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 56277804660147162225
discriminant (Δ): -769627485259860640829419413274073469001875
Faltings height: 6.7161
naive height: 103.9014
primes of bad reduction: 3, 5, 7, 17, 37, 97, 1171
regulator: 2654990.771456044405306004731570871216549925795778127
submitted by: Maksym Voznyy
submitted at: 2026-10-25 15:43:37 UTC
last updated: 2026-10-25 15:43:37 UTC

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

(40019277003771/6497401, -229161523814339801431/16561875149)
(200726062159/81, 89930218053551921/729)
(57588609/16, -134551866209/64)
(48909049/4, 338073602289/8)
(6555031, -15474205842)
(40097691250561/876096, -253853661541769014337/820025856)
(4396896888591/82369, 9218476579030752650/23639903)

Commentary

Voznyy (2026), A = -2500617805, [r, s, t] = [45, 97, 105] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 15:43:37 UTC · history

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